Daily Papers

Process Reward Models (PRMs) have proven effective at enhancing mathematical reasoning for Large Language Models (LLMs) by leveraging increased inference-time computation. However, they are predominantly trained on mathematical data and their generalizability to non-mathematical domains has not been rigorously studied. In response, this work first shows that current PRMs have poor performance in other domains. To address this limitation, we introduce VersaPRM, a multi-domain PRM trained on synthetic reasoning data generated using our novel data generation and annotation method. VersaPRM achieves consistent performance gains across diverse domains. For instance, in the MMLU-Pro category of Law, VersaPRM via weighted majority voting, achieves a 7.9% performance gain over the majority voting baseline -- surpassing Qwen2.5-Math-PRM's gain of 1.3%. We further contribute to the community by open-sourcing all data, code and models for VersaPRM.

This paper presents AlphaSpace, a novel methodology designed to enhance the spatial reasoning capabilities of large language models (LLMs) for 3D Cartesian space navigation. AlphaSpace employs a semantics-based tokenization strategy, encoding height information through specialized semantic tokens, and integrates primarily symbolic synthetic reasoning data. This approach enables LLMs to accurately manipulate objects by positioning them at specific [x, y, z] coordinates. Experimental results demonstrate that AlphaSpace significantly outperforms existing models on manipulation subtasks, achieving a total accuracy of 66.67%, compared to 37.5% for GPT-4o and 29.17% for Claude 3.5 Sonnet.

In this paper, we address the challenge of enforcing strict schema adherence in large language model (LLM) generation by leveraging LLM reasoning capabilities. Building on the DeepSeek R1 reinforcement learning framework, our approach trains structured reasoning skills of a 1.5B parameter model through a novel pipeline that combines synthetic reasoning dataset construction with custom reward functions under Group Relative Policy Optimization (GRPO). Specifically, we first perform R1 reinforcement learning on a 20K sample unstructured-to-structured dataset, mirroring the original DeepSeek R1 methods, to establish core reasoning abilities. Subsequently, we performed supervised fine-tuning on a separate 10K reasoning sample dataset, focusing on refining schema adherence for downstream tasks. Despite the relatively modest training scope, requiring approximately 20 hours on an 8xH100 GPU cluster for GRPO training and 3 hours on 1xA100 for SFT, our model demonstrates robust performance in enforcing schema consistency. We compare our ThinkJSON approach against the original DeepSeek R1 (671B), distilled versions of DeepSeek R1 (Qwen-1.5B and Qwen-7B), and Gemini 2.0 Flash (70B), showcasing its effectiveness in real-world applications. Our results underscore the practical utility of a resource-efficient framework for schema-constrained text generation.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

Large language models (LLMs), both proprietary and open-source, have demonstrated remarkable capabilities across various natural language processing tasks. However, they face significant limitations in legal reasoning tasks. Proprietary models introduce data privacy risks and high inference costs, while open-source models underperform due to insufficient legal domain training data. To address these limitations, we study data generation for legal reasoning to improve the legal reasoning performance of open-source LLMs with the help of proprietary LLMs. This is challenging due to the lack of legal knowledge in proprietary LLMs and the difficulty in verifying the generated data. We propose KgDG, a knowledge-guided data generation framework for legal reasoning. Our framework enables leveraging legal knowledge to enhance generation diversity and introduces a refinement and verification process to ensure the quality of generated data. Moreover, we expand the generated dataset to further enhance the LLM reasoning capabilities. Using KgDG, we create a synthetic legal reasoning dataset containing 50K high-quality examples. Our trained model LawGPT outperforms existing legal-specific LLMs and achieves performance comparable to proprietary LLMs, demonstrating the effectiveness of KgDG and LawGPT. Our code and resources is publicly available at https://anonymous.4open.science/r/KgDG-45F5 .

Reasoning over tabular data requires both table structure understanding and a broad set of table reasoning skills. Current models with table-specific architectures and pre-training methods perform well on understanding table structures, but they still struggle with tasks that require various table reasoning skills. In this work, we develop ReasTAP to show that high-level table reasoning skills can be injected into models during pre-training without a complex table-specific architecture design. We define 7 table reasoning skills, such as numerical operation, temporal comparison, and conjunction. Each reasoning skill is associated with one example generator, which synthesizes questions over semi-structured tables according to the sampled templates. We model the table pre-training task as a sequence generation task and pre-train ReasTAP to generate precise answers to the synthetic examples. ReasTAP is evaluated on four benchmarks covering three downstream tasks including: 1) WikiSQL and WTQ for Table Question Answering; 2) TabFact for Table Fact Verification; and 3) LogicNLG for Faithful Table-to-Text Generation. Experimental results demonstrate that ReasTAP achieves new state-of-the-art performance on all benchmarks and delivers a significant improvement on low-resource setting. Our code is publicly available at https://github.com/Yale-LILY/ReasTAP.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Synthesizing high-quality reasoning data for continual training has been proven to be effective in enhancing the performance of Large Language Models (LLMs). However, previous synthetic approaches struggle to easily scale up data and incur high costs in the pursuit of high quality. In this paper, we propose the Graph-based Synthetic Data Pipeline (GSDP), an economical and scalable framework for high-quality reasoning data synthesis. Inspired by knowledge graphs, we extracted knowledge points from seed data and constructed a knowledge point relationships graph to explore their interconnections. By exploring the implicit relationships among knowledge, our method achieves times255 data expansion. Furthermore, GSDP led by open-source models, achieves synthesis quality comparable to GPT-4-0613 while maintaining times100 lower costs. To tackle the most challenging mathematical reasoning task, we present the GSDP-MATH dataset comprising over 1.91 million pairs of math problems and answers. After fine-tuning on GSDP-MATH, GSDP-7B based on Mistral-7B achieves 37.7% accuracy on MATH and 78.4% on GSM8K, demonstrating the effectiveness of our method. The dataset and models trained in this paper will be available.

Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. In this paper, we introduce MathGenie, a novel method for generating diverse and reliable math problems from a small-scale problem-solution dataset (denoted as seed data). We augment the ground-truth solutions of our seed data and train a back-translation model to translate the augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for the new questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based strategy for solution verification. Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique, resulting in a family of models known as MathGenieLM. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenieLM-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score among open-source language models.

Synthetic high-quality multi-step reasoning data can significantly enhance the performance of large language models on various tasks. However, most existing methods rely on rejection sampling, which generates trajectories independently and suffers from inefficiency and imbalanced sampling across problems of varying difficulty. In this work, we introduce FastMCTS, an innovative data synthesis strategy inspired by Monte Carlo Tree Search. FastMCTS provides a more efficient sampling method for multi-step reasoning data, offering step-level evaluation signals and promoting balanced sampling across problems of different difficulty levels. Experiments on both English and Chinese reasoning datasets demonstrate that FastMCTS generates over 30\% more correct reasoning paths compared to rejection sampling as the number of generated tokens scales up. Furthermore, under comparable synthetic data budgets, models trained on FastMCTS-generated data outperform those trained on rejection sampling data by 3.9\% across multiple benchmarks. As a lightweight sampling strategy, FastMCTS offers a practical and efficient alternative for synthesizing high-quality reasoning data. Our code will be released soon.

Recent advancements in large language models (LLMs) have shown promise in medical applications such as disease diagnosis and treatment planning. However, most existing medical LLMs struggle with the advanced reasoning required for complex clinical scenarios, such as differential diagnosis or personalized treatment suggestions. We proposed FineMedLM-o1, which leverages high-quality synthetic medical data and long-form reasoning data for Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO), enabling advanced dialogue and deep reasoning capabilities. Additionally, we introduced Test-Time Training (TTT) in the medical domain for the first time, facilitating domain adaptation and ensuring reliable, accurate reasoning. Experimental results demonstrate that FineMedLM-o1 achieves a 23% average performance improvement over prior models on key medical benchmarks. Furthermore, the introduction of TTT provides an additional 14% performance boost, highlighting its effectiveness in enhancing medical reasoning capabilities. To support this process, we also proposed a novel method for synthesizing medical dialogue. Compared to other open-source datasets, our dataset stands out as superior in both quality and complexity. The project and data will be released on GitHub.

Question-answering datasets require a broad set of reasoning skills. We show how to use question decompositions to teach language models these broad reasoning skills in a robust fashion. Specifically, we use widely available QDMR representations to programmatically create hard-to-cheat synthetic contexts for real questions in six multi-step reasoning datasets. These contexts are carefully designed to avoid reasoning shortcuts prevalent in real contexts that prevent models from learning the right skills. This results in a pretraining dataset, named TeaBReaC, containing 525K multi-step questions (with associated formal programs) covering about 900 reasoning patterns. We show that pretraining standard language models (LMs) on TeaBReaC before fine-tuning them on target datasets improves their performance by up to 13 F1 points across 4 multi-step QA datasets, with up to 21 point gain on more complex questions. The resulting models also demonstrate higher robustness, with a 5-8 F1 point improvement on two contrast sets. Furthermore, TeaBReaC pretraining substantially improves model performance and robustness even when starting with numerate LMs pretrained using recent methods (e.g., PReasM, POET). Our work thus shows how to effectively use decomposition-guided contexts to robustly teach multi-step reasoning.

Large language models show improved downstream task performance when prompted to generate step-by-step reasoning to justify their final answers. These reasoning steps greatly improve model interpretability and verification, but objectively studying their correctness (independent of the final answer) is difficult without reliable methods for automatic evaluation. We simply do not know how often the stated reasoning steps actually support the final end task predictions. In this work, we present ROSCOE, a suite of interpretable, unsupervised automatic scores that improve and extend previous text generation evaluation metrics. To evaluate ROSCOE against baseline metrics, we design a typology of reasoning errors and collect synthetic and human evaluation scores on commonly used reasoning datasets. In contrast with existing metrics, ROSCOE can measure semantic consistency, logicality, informativeness, fluency, and factuality - among other traits - by leveraging properties of step-by-step rationales. We empirically verify the strength of our metrics on five human annotated and six programmatically perturbed diagnostics datasets - covering a diverse set of tasks that require reasoning skills and show that ROSCOE can consistently outperform baseline metrics.

Complex reasoning is an impressive ability shown by large language models (LLMs). Most LLMs are skilled in deductive reasoning, such as chain-of-thought prompting or iterative tool-using to solve challenging tasks step-by-step. In this paper, we hope to focus on evaluating and teaching LLMs to conduct inductive reasoning, that is, LLMs are supposed to infer underlying rules by observing examples or sequential transformations. However, collecting large-scale and diverse human-generated inductive data is challenging. We focus on data synthesis in the code domain and propose a Case2Code task by exploiting the expressiveness and correctness of programs. Specifically, we collect a diverse set of executable programs, synthesize input-output transformations for each program, and force LLMs to infer the underlying code implementations based on the synthetic I/O cases. We first evaluate representative LLMs on the synthesized Case2Code task and demonstrate that the Case-to-code induction is challenging for LLMs. Then, we synthesize large-scale Case2Code training samples to train LLMs to perform inductive reasoning. Experimental results show that such induction training benefits not only in distribution Case2Code performance but also enhances various coding abilities of trained LLMs, demonstrating the great potential of learning inductive reasoning via synthetic data.

Semantic parsing, which converts natural language questions into logic forms, plays a crucial role in reasoning within structured environments. However, existing methods encounter two significant challenges: reliance on extensive manually annotated datasets and limited generalization capability to unseen examples. To tackle these issues, we propose Targeted Synthetic Data Generation (TARGA), a practical framework that dynamically generates high-relevance synthetic data without manual annotation. Starting from the pertinent entities and relations of a given question, we probe for the potential relevant queries through layer-wise expansion and cross-layer combination. Then we generate corresponding natural language questions for these constructed queries to jointly serve as the synthetic demonstrations for in-context learning. Experiments on multiple knowledge base question answering (KBQA) datasets demonstrate that TARGA, using only a 7B-parameter model, substantially outperforms existing non-fine-tuned methods that utilize close-sourced model, achieving notable improvements in F1 scores on GrailQA(+7.7) and KBQA-Agent(+12.2). Furthermore, TARGA also exhibits superior sample efficiency, robustness, and generalization capabilities under non-I.I.D. settings.

Multimodal counterfactual reasoning is a vital yet challenging ability for AI systems. It involves predicting the outcomes of hypothetical circumstances based on vision and language inputs, which enables AI models to learn from failures and explore hypothetical scenarios. Despite its importance, there are only a few datasets targeting the counterfactual reasoning abilities of multimodal models. Among them, they only cover reasoning over synthetic environments or specific types of events (e.g. traffic collisions), making them hard to reliably benchmark the model generalization ability in diverse real-world scenarios and reasoning dimensions. To overcome these limitations, we develop a video question answering dataset, ACQUIRED: it consists of 3.9K annotated videos, encompassing a wide range of event types and incorporating both first and third-person viewpoints, which ensures a focus on real-world diversity. In addition, each video is annotated with questions that span three distinct dimensions of reasoning, including physical, social, and temporal, which can comprehensively evaluate the model counterfactual abilities along multiple aspects. We benchmark our dataset against several state-of-the-art language-only and multimodal models and experimental results demonstrate a significant performance gap (>13%) between models and humans. The findings suggest that multimodal counterfactual reasoning remains an open challenge and ACQUIRED is a comprehensive and reliable benchmark for inspiring future research in this direction.

Vision-Language Models (VLMs) excel at understanding single images, aided by high-quality instruction datasets. However, multi-image reasoning remains underexplored in the open-source community due to two key challenges: (1) scaling datasets with correlated images and complex reasoning instructions is resource-intensive, and (2) robust evaluation benchmarks for multi-image tasks are lacking. To address this, we introduce SMiR, a synthetic data-generation pipeline for multi-image reasoning, along with a high-quality dataset generated using this pipeline. SMiR efficiently extracts correlated images via multimodal embeddings, integrates visual and descriptive information, and leverages open-source LLMs to generate quality instructions. Using this approach, we produce 160K synthetic training samples, offering a cost-effective alternative to closed-source solutions. Additionally, we present SMiR-Bench, a multi-image reasoning benchmark comprising 200 diverse examples across seven complex reasoning tasks. SMiR-Bench is multi-turn and employs a VLM judge to evaluate free-form responses, providing a comprehensive assessment of model expressiveness and reasoning capability across modalities. We demonstrate the effectiveness of SMiR by fine-tuning open-source VLMs and evaluating them on SMiR-Bench.

Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by building a conceptual understanding of our observations. First, we find that while the typical approach of finetuning a model on synthetic correct or positive problem-solution pairs generated by capable models offers modest performance gains, sampling more correct solutions from the finetuned learner itself followed by subsequent fine-tuning on this self-generated data doubles the efficiency of the same synthetic problems. At the same time, training on model-generated positives can amplify various spurious correlations, resulting in flat or even inverse scaling trends as the amount of data increases. Surprisingly, we find that several of these issues can be addressed if we also utilize negative responses, i.e., model-generated responses that are deemed incorrect by a final answer verifier. Crucially, these negatives must be constructed such that the training can appropriately recover the utility or advantage of each intermediate step in the negative response. With this per-step scheme, we are able to attain consistent gains over only positive data, attaining performance similar to amplifying the amount of synthetic data by 8 times. We show that training on per-step negatives can help to unlearn spurious correlations in the positive data, and is equivalent to advantage-weighted reinforcement learning (RL), implying that it inherits robustness benefits of RL over imitating positive data alone.

Retrieval-Augmented Generation (RAG) systems face significant performance gaps when applied to technical domains requiring precise information extraction from complex documents. Current evaluation methodologies relying on document-level metrics inadequately capture token-resolution retrieval accuracy that is critical for domain-related documents. We propose a framework combining granular evaluation metrics with synthetic data generation to optimize domain-specific RAG performance. First, we introduce token-aware metrics Precision Omega and Intersection-over-Union (IoU) that quantify context preservation versus information density trade-offs inherent in technical texts. Second, we develop a reasoning model-driven pipeline using instruction-tuned LLMs (DeepSeek-R1, DeepSeek-R1 distilled variants, and Phi-4) to generate context-anchored QA pairs with discontinuous reference spans across three specialized corpora: SEC 10-K filings (finance), biomedical abstracts (PubMed), and APT threat reports (cybersecurity). Our empirical analysis reveals critical insights: smaller chunks (less than 10 tokens) improve precision by 31-42% (IoU = 0.071 vs. baseline 0.053) at recall costs (-18%), while domain-specific embedding strategies yield 22% variance in optimal chunk sizing (5-20 tokens). The DeepSeek-R1-Distill-Qwen-32B model demonstrates superior concept alignment (+14% mean IoU over alternatives), though no configuration universally dominates. Financial texts favor larger chunks for risk factor coverage (Recall = 0.81 at size = 20), whereas cybersecurity content benefits from atomic segmentation, Precision Omega = 0.28 at size = 5. Our code is available on https://github.com/aryan-jadon/Synthetic-Data-Generation-and-Evaluation-using-Reasoning-Model

Understanding time series is crucial for its application in real-world scenarios. Recently, large language models (LLMs) have been increasingly applied to time series tasks, leveraging their strong language capabilities to enhance various applications. However, research on multimodal LLMs (MLLMs) for time series understanding and reasoning remains limited, primarily due to the scarcity of high-quality datasets that align time series with textual information. This paper introduces ChatTS, a novel MLLM designed for time series analysis. ChatTS treats time series as a modality, similar to how vision MLLMs process images, enabling it to perform both understanding and reasoning with time series. To address the scarcity of training data, we propose an attribute-based method for generating synthetic time series with detailed attribute descriptions. We further introduce Time Series Evol-Instruct, a novel approach that generates diverse time series Q&As, enhancing the model's reasoning capabilities. To the best of our knowledge, ChatTS is the first MLLM that takes multivariate time series as input, which is fine-tuned exclusively on synthetic datasets. We evaluate its performance using benchmark datasets with real-world data, including six alignment tasks and four reasoning tasks. Our results show that ChatTS significantly outperforms existing vision-based MLLMs (e.g., GPT-4o) and text/agent-based LLMs, achieving a 46.0% improvement in alignment tasks and a 25.8% improvement in reasoning tasks.

Advancements in LLMs have significantly expanded their capabilities across various domains. However, mathematical reasoning remains a challenging area, prompting the development of math-specific LLMs. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and post-training with problem datasets for SFT. Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. This study addresses this discrepancy by exploring alternative strategies during the pre-training phase, focusing on the use of problem-solving data over general mathematical corpora. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? (3) How do the capabilities developed from the same problem-solving data differ between the CPT and SFT stages, and what factors contribute to these differences? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for hard multi-step problem-solving data. These insights provide valuable guidance for optimizing the mathematical reasoning capabilities of LLMs, culminating in our development of a powerful mathematical base model called JiuZhang-8B.

We propose a novel persona-driven data synthesis methodology that leverages various perspectives within a large language model (LLM) to create diverse synthetic data. To fully exploit this methodology at scale, we introduce Persona Hub -- a collection of 1 billion diverse personas automatically curated from web data. These 1 billion personas (~13% of the world's total population), acting as distributed carriers of world knowledge, can tap into almost every perspective encapsulated within the LLM, thereby facilitating the creation of diverse synthetic data at scale for various scenarios. By showcasing Persona Hub's use cases in synthesizing high-quality mathematical and logical reasoning problems, instructions (i.e., user prompts), knowledge-rich texts, game NPCs and tools (functions) at scale, we demonstrate persona-driven data synthesis is versatile, scalable, flexible, and easy to use, potentially driving a paradigm shift in synthetic data creation and applications in practice, which may have a profound impact on LLM research and development.

Large Language Models still struggle in challenging scenarios that leverage structured data, complex reasoning, or tool usage. In this paper, we propose Source2Synth: a new method that can be used for teaching LLMs new skills without relying on costly human annotations. Source2Synth takes as input a custom data source and produces synthetic data points with intermediate reasoning steps grounded in real-world sources. Source2Synth improves the dataset quality by discarding low-quality generations based on their answerability. We demonstrate the generality of this approach by applying it to two challenging domains: we test reasoning abilities in multi-hop question answering (MHQA), and tool usage in tabular question answering (TQA). Our method improves performance by 25.51% for TQA on WikiSQL and 22.57% for MHQA on HotPotQA compared to the fine-tuned baselines.

Question Answering (QA) datasets have been instrumental in developing and evaluating Large Language Model (LLM) capabilities. However, such datasets are scarce for languages other than English due to the cost and difficulties of collection and manual annotation. This means that producing novel models and measuring the performance of multilingual LLMs in low-resource languages is challenging. To mitigate this, we propose SynDARin, a method for generating and validating QA datasets for low-resource languages. We utilize parallel content mining to obtain human-curated paragraphs between English and the target language. We use the English data as context to generate synthetic multiple-choice (MC) question-answer pairs, which are automatically translated and further validated for quality. Combining these with their designated non-English human-curated paragraphs form the final QA dataset. The method allows to maintain the content quality, reduces the likelihood of factual errors, and circumvents the need for costly annotation. To test the method, we created a QA dataset with 1.2K samples for the Armenian language. The human evaluation shows that 98% of the generated English data maintains quality and diversity in the question types and topics, while the translation validation pipeline can filter out sim70% of data with poor quality. We use the dataset to benchmark state-of-the-art LLMs, showing their inability to achieve human accuracy with some model performances closer to random chance. This shows that the generated dataset is non-trivial and can be used to evaluate reasoning capabilities in low-resource language.

We introduce FigureQA, a visual reasoning corpus of over one million question-answer pairs grounded in over 100,000 images. The images are synthetic, scientific-style figures from five classes: line plots, dot-line plots, vertical and horizontal bar graphs, and pie charts. We formulate our reasoning task by generating questions from 15 templates; questions concern various relationships between plot elements and examine characteristics like the maximum, the minimum, area-under-the-curve, smoothness, and intersection. To resolve, such questions often require reference to multiple plot elements and synthesis of information distributed spatially throughout a figure. To facilitate the training of machine learning systems, the corpus also includes side data that can be used to formulate auxiliary objectives. In particular, we provide the numerical data used to generate each figure as well as bounding-box annotations for all plot elements. We study the proposed visual reasoning task by training several models, including the recently proposed Relation Network as a strong baseline. Preliminary results indicate that the task poses a significant machine learning challenge. We envision FigureQA as a first step towards developing models that can intuitively recognize patterns from visual representations of data.

We introduce Generalized Instruction Tuning (called GLAN), a general and scalable method for instruction tuning of Large Language Models (LLMs). Unlike prior work that relies on seed examples or existing datasets to construct instruction tuning data, GLAN exclusively utilizes a pre-curated taxonomy of human knowledge and capabilities as input and generates large-scale synthetic instruction data across all disciplines. Specifically, inspired by the systematic structure in human education system, we build the taxonomy by decomposing human knowledge and capabilities to various fields, sub-fields and ultimately, distinct disciplines semi-automatically, facilitated by LLMs. Subsequently, we generate a comprehensive list of subjects for every discipline and proceed to design a syllabus tailored to each subject, again utilizing LLMs. With the fine-grained key concepts detailed in every class session of the syllabus, we are able to generate diverse instructions with a broad coverage across the entire spectrum of human knowledge and skills. Extensive experiments on large language models (e.g., Mistral) demonstrate that GLAN excels in multiple dimensions from mathematical reasoning, coding, academic exams, logical reasoning to general instruction following without using task-specific training data of these tasks. In addition, GLAN allows for easy customization and new fields or skills can be added by simply incorporating a new node into our taxonomy.

Contrastive Language-Image Pretraining (CLIP) models maximize the mutual information between text and visual modalities to learn representations. This makes the nature of the training data a significant factor in the efficacy of CLIP for downstream tasks. However, the lack of compositional diversity in contemporary image-text datasets limits the compositional reasoning ability of CLIP. We show that generating ``hard'' negative captions via in-context learning and synthesizing corresponding negative images with text-to-image generators offers a solution. We introduce a novel contrastive pre-training strategy that leverages these hard negative captions and images in an alternating fashion to train CLIP. We demonstrate that our method, named TripletCLIP, when applied to existing datasets such as CC3M and CC12M, enhances the compositional capabilities of CLIP, resulting in an absolute improvement of over 9% on the SugarCrepe benchmark on an equal computational budget, as well as improvements in zero-shot image classification and image retrieval. Our code, models, and data are available at: https://tripletclip.github.io

Intellecta dataset emerges as an innovative synthetic dataset, engineered to enhance the cognitive processing capabilities of contemporary language models. With a composition of 11.53 billion tokens, integrating 8.01 billion tokens of synthetic data with 3.52 billion tokens of rich textbook data, Intellecta is crafted to foster advanced reasoning and comprehensive educational narrative generation. Leveraging the Mixtral-8x7B-Instruct-v0.1 model, the dataset facilitates the generation of complex thought processes and detailed, textbook-style explanations, thus enabling language models to engage in both critical thinking and profound educational discourse. This hybrid dataset stands as a testament to the potential of synthetic data in pushing the boundaries of AI, offering a repository that is not only vast and varied but also refined to align with ethical standards and intellectual rigor.

Reasoning about images with rich text, such as charts and documents, is a critical application of vision-language models (VLMs). However, VLMs often struggle in these domains due to the scarcity of diverse text-rich vision-language data. To address this challenge, we present CoSyn, a framework that leverages the coding capabilities of text-only large language models (LLMs) to automatically create synthetic text-rich multimodal data. Given input text describing a target domain (e.g., "nutrition fact labels"), CoSyn prompts an LLM to generate code (Python, HTML, LaTeX, etc.) for rendering synthetic images. With the underlying code as textual representations of the synthetic images, CoSyn can generate high-quality instruction-tuning data, again relying on a text-only LLM. Using CoSyn, we constructed a dataset comprising 400K images and 2.7M rows of vision-language instruction-tuning data. Comprehensive experiments on seven benchmarks demonstrate that models trained on our synthetic data achieve state-of-the-art performance among competitive open-source models, including Llama 3.2, and surpass proprietary models such as GPT-4V and Gemini 1.5 Flash. Furthermore, CoSyn can produce synthetic pointing data, enabling VLMs to ground information within input images, showcasing its potential for developing multimodal agents capable of acting in real-world environments.

Multimodal large language models (MLLMs) have significantly advanced tasks like caption generation and visual question answering by integrating visual and textual data. However, they sometimes produce misleading or hallucinate content due to discrepancies between their pre-training data and real user prompts. Existing approaches using Direct Preference Optimization (DPO) in vision-language tasks often rely on strong models like GPT-4 or CLIP to determine positive and negative responses. Here, we propose a new framework in generating synthetic data using a reward model as a proxy of human preference for effective multimodal alignment with DPO training. The resulting DPO dataset ranges from 2K to 9K image-text pairs, was evaluated on LLaVA-v1.5-7B, where our approach demonstrated substantial improvements in both the trustworthiness and reasoning capabilities of the base model across multiple hallucination and vision-language benchmark. The experiment results indicate that integrating selected synthetic data, such as from generative and rewards models can effectively reduce reliance on human-annotated data while enhancing MLLMs' alignment capability, offering a scalable solution for safer deployment.

Hallucination has been a major problem for large language models and remains a critical challenge when it comes to multimodality in which vision-language models (VLMs) have to deal with not just textual but also visual inputs. Despite rapid progress in VLMs, resources for evaluating and addressing multimodal hallucination are limited and mostly focused on evaluation. This work introduces HaloQuest, a novel visual question answering dataset that captures various aspects of multimodal hallucination such as false premises, insufficient contexts, and visual challenges. A novel idea from HaloQuest is to leverage synthetic images, apart from real ones, to enable dataset creation at scale. With over 7.7K examples spanning across a wide variety of categories, HaloQuest was designed to be both a challenging benchmark for VLMs and a fine-tuning dataset for advancing multimodal reasoning. Our experiments reveal that current models struggle with HaloQuest, with all open-source VLMs achieving below 36% accuracy. On the other hand, fine-tuning on HaloQuest significantly reduces hallucination rates while preserving performance on standard reasoning tasks. Our results discover that benchmarking with generated images is highly correlated (r=0.97) with real images. Last but not least, we propose a novel Auto-Eval mechanism that is highly correlated with human raters (r=0.99) for evaluating VLMs. In sum, this work makes concrete strides towards understanding, evaluating, and mitigating hallucination in VLMs, serving as an important step towards more reliable multimodal AI systems in the future.

Although most current large multimodal models (LMMs) can already understand photos of natural scenes and portraits, their understanding of abstract images, e.g., charts, maps, or layouts, and visual reasoning capabilities remains quite rudimentary. They often struggle with simple daily tasks, such as reading time from a clock, understanding a flowchart, or planning a route using a road map. In light of this, we design a multi-modal self-instruct, utilizing large language models and their code capabilities to synthesize massive abstract images and visual reasoning instructions across daily scenarios. Our strategy effortlessly creates a multimodal benchmark with 11,193 instructions for eight visual scenarios: charts, tables, simulated maps, dashboards, flowcharts, relation graphs, floor plans, and visual puzzles. This benchmark, constructed with simple lines and geometric elements, exposes the shortcomings of most advanced LMMs like Claude-3.5-Sonnet and GPT-4o in abstract image understanding, spatial relations reasoning, and visual element induction. Besides, to verify the quality of our synthetic data, we fine-tune an LMM using 62,476 synthetic chart, table and road map instructions. The results demonstrate improved chart understanding and map navigation performance, and also demonstrate potential benefits for other visual reasoning tasks. Our code is available at: https://github.com/zwq2018/Multi-modal-Self-instruct.

LLM developers are increasingly reliant on synthetic data, but generating high-quality data for complex long-context reasoning tasks remains challenging. We introduce CLIPPER, a compression-based approach for generating synthetic data tailored to narrative claim verification - a task that requires reasoning over a book to verify a given claim. Instead of generating claims directly from the raw text of the book, which results in artifact-riddled claims, CLIPPER first compresses the book into chapter outlines and book summaries and then uses these intermediate representations to generate complex claims and corresponding chain-of-thoughts. Compared to naive approaches, CLIPPER produces claims that are more valid, grounded, and complex. Using CLIPPER, we construct a dataset of 19K synthetic book claims paired with their source texts and chain-of-thought reasoning, and use it to fine-tune three open-weight models. Our best model achieves breakthrough results on narrative claim verification (from 28% to 76% accuracy on our test set) and sets a new state-of-the-art for sub-10B models on the NoCha leaderboard. Further analysis shows that our models generate more detailed and grounded chain-of-thought reasoning while also improving performance on other narrative understanding tasks (e.g., NarrativeQA).

With the rapid development of AI-generated content, the future internet may be inundated with synthetic data, making the discrimination of authentic and credible multimodal data increasingly challenging. Synthetic data detection has thus garnered widespread attention, and the performance of large multimodal models (LMMs) in this task has attracted significant interest. LMMs can provide natural language explanations for their authenticity judgments, enhancing the explainability of synthetic content detection. Simultaneously, the task of distinguishing between real and synthetic data effectively tests the perception, knowledge, and reasoning capabilities of LMMs. In response, we introduce LOKI, a novel benchmark designed to evaluate the ability of LMMs to detect synthetic data across multiple modalities. LOKI encompasses video, image, 3D, text, and audio modalities, comprising 18K carefully curated questions across 26 subcategories with clear difficulty levels. The benchmark includes coarse-grained judgment and multiple-choice questions, as well as fine-grained anomaly selection and explanation tasks, allowing for a comprehensive analysis of LMMs. We evaluated 22 open-source LMMs and 6 closed-source models on LOKI, highlighting their potential as synthetic data detectors and also revealing some limitations in the development of LMM capabilities. More information about LOKI can be found at https://opendatalab.github.io/LOKI/

Extending the capabilities of Large Language Models (LLMs) with functions or tools for environment interaction has led to the emergence of the agent paradigm. In industry, training an LLM is not always feasible because of the scarcity of domain data, legal holds on proprietary customer data, rapidly changing business requirements, and the need to prototype new assistants. Agents provide an elegant solution to the above by relying on the zero-shot reasoning abilities of the underlying LLM and utilizing tools to explore and reason over customer data and respond to user requests. However, there are two concerns here: (I) acquiring large scale customer queries for agent testing is time-consuming, and (II) high reliance on the tool call sequence (or trajectory) followed by the agent to respond to user queries may lead to unexpected or incorrect behavior. To address this, we propose MAG-V, a multi-agent framework to first generate a dataset of questions that mimic customer queries; and second, reverse-engineer alternate questions from the responses for trajectory verification. Initial results indicate that our synthetic data can improve agent performance on actual customer queries. Furthermore, our trajectory verification methodology, inspired by distant supervision and using traditional machine learning (ML) models, outperforms a GPT-4o judge baseline by 11% accuracy and matches the performance of a GPT-4 judge on our constructed dataset. Overall, our approach is a step towards unifying diverse task agents into a cohesive framework for achieving an aligned objective.

Large language models (LLMs) have shown great potential in complex reasoning tasks, yet their performance is often hampered by the scarcity of high-quality, reasoning-focused training datasets. Addressing this challenge, we propose Key-Point-Driven Data Synthesis (KPDDS), a novel data synthesis framework that synthesizes question-answer pairs by leveraging key points and exemplar pairs from authentic data sources. KPDDS ensures the generation of novel questions with rigorous quality control and substantial scalability. As a result, we present KPMath, the most extensive synthetic dataset tailored for mathematical reasoning to date, comprising over one million question-answer pairs. Utilizing KPMath and augmenting it with additional reasoning-intensive corpora, we create the comprehensive KPMath-Plus dataset. Fine-tuning the Mistral-7B model on KPMath-Plus yields a zero-shot PASS@1 accuracy of 39.3% on the MATH test set, a performance that not only outpaces other finetuned 7B models but also exceeds that of certain 34B models. Our ablation studies further confirm the substantial enhancement in mathematical reasoning across various subtopics, marking a significant stride in LLMs' reasoning capabilities.

The information in tables can be an important complement to text, making table-based question answering (QA) systems of great value. The intrinsic complexity of handling tables often adds an extra burden to both model design and data annotation. In this paper, we aim to develop a simple table-based QA model with minimal annotation effort. Motivated by the fact that table-based QA requires both alignment between questions and tables and the ability to perform complicated reasoning over multiple table elements, we propose an omnivorous pretraining approach that consumes both natural and synthetic data to endow models with these respective abilities. Specifically, given freely available tables, we leverage retrieval to pair them with relevant natural sentences for mask-based pretraining, and synthesize NL questions by converting SQL sampled from tables for pretraining with a QA loss. We perform extensive experiments in both few-shot and full settings, and the results clearly demonstrate the superiority of our model OmniTab, with the best multitasking approach achieving an absolute gain of 16.2% and 2.7% in 128-shot and full settings respectively, also establishing a new state-of-the-art on WikiTableQuestions. Detailed ablations and analyses reveal different characteristics of natural and synthetic data, shedding light on future directions in omnivorous pretraining. Code, pretraining data, and pretrained models are available at https://github.com/jzbjyb/OmniTab.

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem proving is hindered by a lack of training data. To address this issue, we introduce an approach to generate extensive Lean 4 proof data derived from high-school and undergraduate-level mathematical competition problems. This approach involves translating natural language problems into formal statements, filtering out low-quality statements, and generating proofs to create synthetic data. After fine-tuning the DeepSeekMath 7B model on this synthetic dataset, which comprises 8 million formal statements with proofs, our model achieved whole-proof generation accuracies of 46.3% with 64 samples and 52% cumulatively on the Lean 4 miniF2F test, surpassing the baseline GPT-4 at 23.0% with 64 samples and a tree search reinforcement learning method at 41.0%. Additionally, our model successfully proved 5 out of 148 problems in the Lean 4 Formalized International Mathematical Olympiad (FIMO) benchmark, while GPT-4 failed to prove any. These results demonstrate the potential of leveraging large-scale synthetic data to enhance theorem-proving capabilities in LLMs. Both the synthetic dataset and the model will be made available to facilitate further research in this promising field.

We present Synthio, a novel approach for augmenting small-scale audio classification datasets with synthetic data. Our goal is to improve audio classification accuracy with limited labeled data. Traditional data augmentation techniques, which apply artificial transformations (e.g., adding random noise or masking segments), struggle to create data that captures the true diversity present in real-world audios. To address this shortcoming, we propose to augment the dataset with synthetic audio generated from text-to-audio (T2A) diffusion models. However, synthesizing effective augmentations is challenging because not only should the generated data be acoustically consistent with the underlying small-scale dataset, but they should also have sufficient compositional diversity. To overcome the first challenge, we align the generations of the T2A model with the small-scale dataset using preference optimization. This ensures that the acoustic characteristics of the generated data remain consistent with the small-scale dataset. To address the second challenge, we propose a novel caption generation technique that leverages the reasoning capabilities of Large Language Models to (1) generate diverse and meaningful audio captions and (2) iteratively refine their quality. The generated captions are then used to prompt the aligned T2A model. We extensively evaluate Synthio on ten datasets and four simulated limited-data settings. Results indicate our method consistently outperforms all baselines by 0.1%-39% using a T2A model trained only on weakly-captioned AudioSet.

Large-scale pre-trained Vision & Language (VL) models have shown remarkable performance in many applications, enabling replacing a fixed set of supported classes with zero-shot open vocabulary reasoning over (almost arbitrary) natural language prompts. However, recent works have uncovered a fundamental weakness of these models. For example, their difficulty to understand Visual Language Concepts (VLC) that go 'beyond nouns' such as the meaning of non-object words (e.g., attributes, actions, relations, states, etc.), or difficulty in performing compositional reasoning such as understanding the significance of the order of the words in a sentence. In this work, we investigate to which extent purely synthetic data could be leveraged to teach these models to overcome such shortcomings without compromising their zero-shot capabilities. We contribute Synthetic Visual Concepts (SyViC) - a million-scale synthetic dataset and data generation codebase allowing to generate additional suitable data to improve VLC understanding and compositional reasoning of VL models. Additionally, we propose a general VL finetuning strategy for effectively leveraging SyViC towards achieving these improvements. Our extensive experiments and ablations on VL-Checklist, Winoground, and ARO benchmarks demonstrate that it is possible to adapt strong pre-trained VL models with synthetic data significantly enhancing their VLC understanding (e.g. by 9.9% on ARO and 4.3% on VL-Checklist) with under 1% drop in their zero-shot accuracy.

Code verification has recently found great success as a critical component in training large scale reasoning models for coding. Synthetic techniques such as self-generated test cases and reward models provide a way to enhance code capabilities beyond predefined tests. Building on these advancements, we propose new benchmarks designed to systematically evaluate the impact of synthetic verification methods on assessing solution correctness. We introduce HE-R, HE-R+, MBPP-R, and MBPP-R+, which transform existing coding benchmarks into scoring and ranking datasets to evaluate the effectiveness of synthetic verifiers. Using these benchmarks, we analyze synthetic verification methods in standard, reasoning-based, and reward-based LLMs. Our results show that recent reasoning models significantly improve test case generation and that scaling test cases enhances verification accuracy.

We present a novel soft prompt based framework, SoftSRV, that leverages a frozen pre-trained large language model (LLM) to generate targeted synthetic text sequences. Given a sample from the target distribution, our proposed framework uses data-driven loss minimization to train a parameterized "contextual" soft prompt. This soft prompt is then used to steer the frozen LLM to generate synthetic sequences that are similar to the target distribution. We argue that SoftSRV provides a practical improvement over common hard-prompting approaches that rely on human-curated prompt-templates, which can be idiosyncratic, labor-intensive to craft, and may need to be specialized per domain. We empirically evaluate SoftSRV and hard-prompting baselines by generating synthetic data to fine-tune a small Gemma model on three different domains (coding, math, reasoning). To stress the generality of SoftSRV, we perform these evaluations without any particular specialization of the framework to each domain. We find that SoftSRV significantly improves upon hard-prompting baselines, generating data with superior fine-tuning performance and that better matches the target distribution according to the MAUVE similarity metric.

Large Language Models (LLMs) hold immense potential to generate synthetic data of high quality and utility, which has numerous applications from downstream model training to practical data utilisation. However, contemporary models, despite their impressive capacities, consistently struggle to produce both coherent and diverse data. To address the coherency issue, we introduce contrastive expert guidance, where the difference between the logit distributions of fine-tuned and base language models is emphasised to ensure domain adherence. In order to ensure diversity, we utilise existing real and synthetic examples as negative prompts to the model. We deem this dual-pronged approach to logit reshaping as STEER: Semantic Text Enhancement via Embedding Repositioning. STEER operates at inference-time and systematically guides the LLMs to strike a balance between adherence to the data distribution (ensuring semantic fidelity) and deviation from prior synthetic examples or existing real datasets (ensuring diversity and authenticity). This delicate balancing act is achieved by dynamically moving towards or away from chosen representations in the latent space. STEER demonstrates improved performance over previous synthetic data generation techniques, exhibiting better balance between data diversity and coherency across three distinct tasks: hypothesis generation, toxic and non-toxic comment generation, and commonsense reasoning task generation. We demonstrate how STEER allows for fine-tuned control over the diversity-coherency trade-off via its hyperparameters, highlighting its versatility.

Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also demonstrates certain generalization capabilities on the out-of-domain datasets. Specifically, this paper has designed two out-of-domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively.

Recent studies have shown that Large Language Models (LLMs) struggle to accurately retrieve information and maintain reasoning capabilities when processing long-context inputs. To address these limitations, we propose a finetuning approach utilizing a carefully designed synthetic dataset comprising numerical key-value retrieval tasks. Our experiments on models like GPT-3.5 Turbo and Mistral 7B demonstrate that finetuning LLMs on this dataset significantly improves LLMs' information retrieval and reasoning capabilities in longer-context settings. We present an analysis of the finetuned models, illustrating the transfer of skills from synthetic to real task evaluations (e.g., 10.5% improvement on 20 documents MDQA at position 10 for GPT-3.5 Turbo). We also find that finetuned LLMs' performance on general benchmarks remains almost constant while LLMs finetuned on other baseline long-context augmentation data can encourage hallucination (e.g., on TriviaQA, Mistral 7B finetuned on our synthetic data cause no performance drop while other baseline data can cause a drop that ranges from 2.33% to 6.19%). Our study highlights the potential of finetuning on synthetic data for improving the performance of LLMs on longer-context tasks.

Leading open-source large language models (LLMs) such as Llama-3.1-Instruct-405B are extremely capable at generating text, answering questions, and solving a variety of natural language understanding tasks. However, they incur higher inference cost and latency compared to smaller LLMs. Knowledge distillation provides a way to use outputs from these large, capable teacher models to train smaller student models which can be used for inference at lower cost and latency, while retaining comparable accuracy. We investigate the efficacy of distillation using the Llama-3.1-405B-Instruct teacher and the smaller Llama-3.1-8B-Instruct and Llama-3.1-70B-Instruct student models. Contributions of this work include (a) We evaluate the generalizability of distillation with the above Llama-3.1 teacher-student pairs across different tasks and datasets (b) We show that using synthetic data during distillation significantly improves the accuracy of 8B and 70B models, and when used with reasoning chains, even matches or surpasses the zero-shot accuracy of 405B model on some datasets (c) We empirically show that distillation enables 8B and 70B models to internalize 405B's reasoning ability by using only standard fine-tuning (without customizing any loss function). This allows cost and latency-efficient student model inference. (d) We show pitfalls in evaluation of distillation, and present task-specific evaluation, including both human and LLM-grading, and ground-truth based traditional accuracy benchmarks. This methodical study brings out the fundamental importance of synthetic data quality in knowledge distillation, and of combining multiple, task-specific ways of accuracy and quality evaluation in assessing the effectiveness of distillation.

We introduce KodCode, a synthetic dataset that addresses the persistent challenge of acquiring high-quality, verifiable training data across diverse difficulties and domains for training Large Language Models for coding. Existing code-focused resources typically fail to ensure either the breadth of coverage (e.g., spanning simple coding tasks to advanced algorithmic problems) or verifiable correctness (e.g., unit tests). In contrast, KodCode comprises question-solution-test triplets that are systematically validated via a self-verification procedure. Our pipeline begins by synthesizing a broad range of coding questions, then generates solutions and test cases with additional attempts allocated to challenging problems. Finally, post-training data synthesis is done by rewriting questions into diverse formats and generating responses under a test-based reject sampling procedure from a reasoning model (DeepSeek R1). This pipeline yields a large-scale, robust and diverse coding dataset. KodCode is suitable for supervised fine-tuning and the paired unit tests also provide great potential for RL tuning. Fine-tuning experiments on coding benchmarks (HumanEval(+), MBPP(+), BigCodeBench, and LiveCodeBench) demonstrate that KodCode-tuned models achieve state-of-the-art performance, surpassing models like Qwen2.5-Coder-32B-Instruct and DeepSeek-R1-Distill-Llama-70B.

Existing synthetic datasets (FigureQA, DVQA) for reasoning over plots do not contain variability in data labels, real-valued data, or complex reasoning questions. Consequently, proposed models for these datasets do not fully address the challenge of reasoning over plots. In particular, they assume that the answer comes either from a small fixed size vocabulary or from a bounding box within the image. However, in practice, this is an unrealistic assumption because many questions require reasoning and thus have real-valued answers which appear neither in a small fixed size vocabulary nor in the image. In this work, we aim to bridge this gap between existing datasets and real-world plots. Specifically, we propose PlotQA with 28.9 million question-answer pairs over 224,377 plots on data from real-world sources and questions based on crowd-sourced question templates. Further, 80.76% of the out-of-vocabulary (OOV) questions in PlotQA have answers that are not in a fixed vocabulary. Analysis of existing models on PlotQA reveals that they cannot deal with OOV questions: their overall accuracy on our dataset is in single digits. This is not surprising given that these models were not designed for such questions. As a step towards a more holistic model which can address fixed vocabulary as well as OOV questions, we propose a hybrid approach: Specific questions are answered by choosing the answer from a fixed vocabulary or by extracting it from a predicted bounding box in the plot, while other questions are answered with a table question-answering engine which is fed with a structured table generated by detecting visual elements from the image. On the existing DVQA dataset, our model has an accuracy of 58%, significantly improving on the highest reported accuracy of 46%. On PlotQA, our model has an accuracy of 22.52%, which is significantly better than state of the art models.

Large language models (LLMs) learn temporal concepts from the co-occurrence of related tokens in a sequence. Compared with conventional text generation, temporal reasoning, which reaches a conclusion based on mathematical, logical and commonsense knowledge, is more challenging. In this paper, we propose TempGraph-LLM, a new paradigm towards text-based temporal reasoning. To be specific, we first teach LLMs to translate the context into a temporal graph. A synthetic dataset, which is fully controllable and requires minimal supervision, is constructed for pre-training on this task. We prove in experiments that LLMs benefit from the pre-training on other tasks. On top of that, we guide LLMs to perform symbolic reasoning with the strategies of Chain of Thoughts (CoTs) bootstrapping and special data augmentation. We observe that CoTs with symbolic reasoning bring more consistent and reliable results than those using free text.

Multimodal Audio-Language Models (ALMs) can understand and reason over both audio and text. Typically, reasoning performance correlates with model size, with the best results achieved by models exceeding 8 billion parameters. However, no prior work has explored enabling small audio-language models to perform reasoning tasks, despite the potential applications for edge devices. To address this gap, we introduce Mellow, a small Audio-Language Model specifically designed for reasoning. Mellow achieves state-of-the-art performance among existing small audio-language models and surpasses several larger models in reasoning capabilities. For instance, Mellow scores 52.11 on MMAU, comparable to SoTA Qwen2 Audio (which scores 52.5) while using 50 times fewer parameters and being trained on 60 times less data (audio hrs). To train Mellow, we introduce ReasonAQA, a dataset designed to enhance audio-grounded reasoning in models. It consists of a mixture of existing datasets (30% of the data) and synthetically generated data (70%). The synthetic dataset is derived from audio captioning datasets, where Large Language Models (LLMs) generate detailed and multiple-choice questions focusing on audio events, objects, acoustic scenes, signal properties, semantics, and listener emotions. To evaluate Mellow's reasoning ability, we benchmark it on a diverse set of tasks, assessing on both in-distribution and out-of-distribution data, including audio understanding, deductive reasoning, and comparative reasoning. Finally, we conduct extensive ablation studies to explore the impact of projection layer choices, synthetic data generation methods, and language model pretraining on reasoning performance. Our training dataset, findings, and baseline pave the way for developing small ALMs capable of reasoning.

Compute scaling for language model (LM) pretraining has outpaced the growth of human-written texts, leading to concerns that data will become the bottleneck to LM scaling. To continue scaling pretraining in this data-constrained regime, we propose that explicitly modeling and inferring the latent thoughts that underlie the text generation process can significantly improve pretraining data efficiency. Intuitively, our approach views web text as the compressed final outcome of a verbose human thought process and that the latent thoughts contain important contextual knowledge and reasoning steps that are critical to data-efficient learning. We empirically demonstrate the effectiveness of our approach through data-constrained continued pretraining for math. We first show that synthetic data approaches to inferring latent thoughts significantly improve data efficiency, outperforming training on the same amount of raw data (5.7\% rightarrow 25.4\% on MATH). Furthermore, we demonstrate latent thought inference without a strong teacher, where an LM bootstraps its own performance by using an EM algorithm to iteratively improve the capability of the trained LM and the quality of thought-augmented pretraining data. We show that a 1B LM can bootstrap its performance across at least three iterations and significantly outperform baselines trained on raw data, with increasing gains from additional inference compute when performing the E-step. The gains from inference scaling and EM iterations suggest new opportunities for scaling data-constrained pretraining.

Incorporating external knowledge in large language models (LLMs) enhances their utility across diverse applications, but existing methods have trade-offs. Retrieval-Augmented Generation (RAG) fetches evidence via similarity search, but key information may fall outside top ranked results. Long-context models can process multiple documents but are computationally expensive and limited by context window size. Inspired by students condensing study material for open-book exams, we propose task-aware key-value (KV) cache compression, which compresses external knowledge in a zero- or few-shot setup. This enables LLMs to reason efficiently over a compacted representation of all relevant information. Experiments show our approach outperforms both RAG and task-agnostic compression methods. On LongBench v2, it improves accuracy by up to 7 absolute points over RAG with a 30x compression rate, while reducing inference latency from 0.43s to 0.16s. A synthetic dataset highlights that RAG performs well when sparse evidence suffices, whereas task-aware compression is superior for broad knowledge tasks.

Enabling effective collaboration among LLMs is a crucial step toward developing autonomous systems capable of solving complex problems. While LLMs are typically used as single-model generators, where humans critique and refine their outputs, the potential for jointly-trained collaborative models remains largely unexplored. Despite promising results in multi-agent communication and debate settings, little progress has been made in training models to work together on tasks. In this paper, we present a first step toward "Multi-agent LLM training" (MALT) on reasoning problems. Our approach employs a sequential multi-agent setup with heterogeneous LLMs assigned specialized roles: a generator, verifier, and refinement model iteratively solving problems. We propose a trajectory-expansion-based synthetic data generation process and a credit assignment strategy driven by joint outcome based rewards. This enables our post-training setup to utilize both positive and negative trajectories to autonomously improve each model's specialized capabilities as part of a joint sequential system. We evaluate our approach across MATH, GSM8k, and CQA, where MALT on Llama 3.1 8B models achieves relative improvements of 14.14%, 7.12%, and 9.40% respectively over the same baseline model. This demonstrates an early advance in multi-agent cooperative capabilities for performance on mathematical and common sense reasoning questions. More generally, our work provides a concrete direction for research around multi-agent LLM training approaches.

The rapid advancement of large language models (LLMs) has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate LLMs' strategic reasoning capabilities, game theory, with its concise structure, has become a preferred approach. However, current research focuses on a limited selection of games, resulting in low coverage. Classic game scenarios risk data leakage, and existing benchmarks often lack extensibility, making them inadequate for evaluating state-of-the-art models. To address these challenges, we propose TMGBench, a benchmark with comprehensive game type coverage, novel scenarios, and flexible organization. Specifically, we incorporate all 144 game types summarized by the Robinson-Goforth topology of 2x2 games, constructed as classic games. We also employ synthetic data generation to create diverse, higher-quality scenarios through topic guidance and human inspection, referred to as story-based games. Lastly, we provide a sustainable framework for increasingly powerful LLMs by treating these games as atomic units and organizing them into more complex forms via sequential, parallel, and nested structures. Our comprehensive evaluation of mainstream LLMs covers tests on rational reasoning, robustness, Theory-of-Mind (ToM), and reasoning in complex forms. Results reveal flaws in accuracy, consistency, and varying mastery of ToM. Additionally, o1-mini, OpenAI's latest reasoning model, achieved accuracy rates of 66.6%, 60.0%, and 70.0% on sequential, parallel, and nested games, highlighting TMGBench's challenges.

While open-source multi-modal language models perform well on simple question answering tasks, they often fail on complex questions that require multiple capabilities, such as fine-grained recognition, visual grounding, and reasoning, and that demand multi-step solutions. We present TACO, a family of multi-modal large action models designed to improve performance on such complex, multi-step, and multi-modal tasks. During inference, TACO produces chains-of-thought-and-action (CoTA), executes intermediate steps by invoking external tools such as OCR, depth estimation and calculator, then integrates both the thoughts and action outputs to produce coherent responses. To train TACO, we create a large dataset of over 1M synthetic CoTA traces generated with GPT-4o and Python programs. We then experiment with various data filtering and mixing techniques and obtain a final subset of 293K high-quality CoTA examples. This dataset enables TACO to learn complex reasoning and action paths, surpassing existing models trained on instruction tuning data with only direct answers. Our model TACO outperforms the instruction-tuned baseline across 8 benchmarks, achieving a 3.6% improvement on average, with gains of up to 15% in MMVet tasks involving OCR, mathematical reasoning, and spatial reasoning. Training on high-quality CoTA traces sets a new standard for complex multi-modal reasoning, highlighting the need for structured, multi-step instruction tuning in advancing open-source mutli-modal models' capabilities.

We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path and derive the final answer. We handle the limitations of existed works in two folds: 1) enhance the interpretability of reasoning procedures with detailed tracking, by predicting nodes and edges in the proof path iteratively backward from the question; 2) promote the efficiency and accuracy via reasoning on the elaborate representations of nodes and history paths, without any intermediate texts that may introduce external noise during proof generation. There are three main modules in IBR, QA and proof strategy prediction to obtain the answer and offer guidance for the following procedure; parent node prediction to determine a node in the existing proof that a new child node will link to; child node prediction to find out which new node will be added to the proof. Experiments on both synthetic and paraphrased datasets demonstrate that IBR has better in-domain performance as well as cross-domain transferability than several strong baselines. Our code and models are available at https://github.com/find-knowledge/IBR .

This paper introduces Typhoon T1, an open effort to develop an open Thai reasoning model. A reasoning model is a relatively new type of generative model built on top of large language models (LLMs). A reasoning model generates a long chain of thought before arriving at a final answer, an approach found to improve performance on complex tasks. However, details on developing such a model are limited, especially for reasoning models that can generate traces in a low-resource language. Typhoon T1 presents an open effort that dives into the details of developing a reasoning model in a more cost-effective way by leveraging supervised fine-tuning using open datasets, instead of reinforcement learning. This paper shares the details about synthetic data generation and training, as well as our dataset and model weights. Additionally, we provide insights gained from developing a reasoning model that generalizes across domains and is capable of generating reasoning traces in a low-resource language, using Thai as an example. We hope this open effort provides a foundation for further research in this field.

This paper introduces TinyEmo, a family of small multi-modal language models for emotional reasoning and classification. Our approach features: (1) a synthetic emotional instruct dataset for both pre-training and fine-tuning stages, (2) a Metric Projector that delegates classification from the language model allowing for more efficient training and inference, (3) a multi-modal large language model (MM-LLM) for emotional reasoning, and (4) a semi-automated framework for bias detection. TinyEmo is able to perform emotion classification and emotional reasoning, all while using substantially fewer parameters than comparable models. This efficiency allows us to freely incorporate more diverse emotional datasets, enabling strong performance on classification tasks, with our smallest model (700M parameters) outperforming larger state-of-the-art models based on general-purpose MM-LLMs with over 7B parameters. Additionally, the Metric Projector allows for interpretability and indirect bias detection in large models without additional training, offering an approach to understand and improve AI systems. We release code, models, and dataset at https://github.com/ggcr/TinyEmo

While recent advancements in commercial large language models (LM) have shown promising results in medical tasks, their closed-source nature poses significant privacy and security concerns, hindering their widespread use in the medical field. Despite efforts to create open-source models, their limited parameters often result in insufficient multi-step reasoning capabilities required for solving complex medical problems. To address this, we introduce Meerkat-7B, a novel medical AI system with 7 billion parameters. Meerkat-7B was trained using our new synthetic dataset consisting of high-quality chain-of-thought reasoning paths sourced from 18 medical textbooks, along with diverse instruction-following datasets. Our system achieved remarkable accuracy across seven medical benchmarks, surpassing GPT-3.5 by 13.1%, as well as outperforming the previous best 7B models such as MediTron-7B and BioMistral-7B by 13.4% and 9.8%, respectively. Notably, it surpassed the passing threshold of the United States Medical Licensing Examination (USMLE) for the first time for a 7B-parameter model. Additionally, our system offered more detailed free-form responses to clinical queries compared to existing 7B and 13B models, approaching the performance level of GPT-3.5. This significantly narrows the performance gap with large LMs, showcasing its effectiveness in addressing complex medical challenges.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

Performing robotic grasping from a cluttered bin based on human instructions is a challenging task, as it requires understanding both the nuances of free-form language and the spatial relationships between objects. Vision-Language Models (VLMs) trained on web-scale data, such as GPT-4o, have demonstrated remarkable reasoning capabilities across both text and images. But can they truly be used for this task in a zero-shot setting? And what are their limitations? In this paper, we explore these research questions via the free-form language-based robotic grasping task, and propose a novel method, FreeGrasp, leveraging the pre-trained VLMs' world knowledge to reason about human instructions and object spatial arrangements. Our method detects all objects as keypoints and uses these keypoints to annotate marks on images, aiming to facilitate GPT-4o's zero-shot spatial reasoning. This allows our method to determine whether a requested object is directly graspable or if other objects must be grasped and removed first. Since no existing dataset is specifically designed for this task, we introduce a synthetic dataset FreeGraspData by extending the MetaGraspNetV2 dataset with human-annotated instructions and ground-truth grasping sequences. We conduct extensive analyses with both FreeGraspData and real-world validation with a gripper-equipped robotic arm, demonstrating state-of-the-art performance in grasp reasoning and execution. Project website: https://tev-fbk.github.io/FreeGrasp/.

While recent AI-for-math has made strides in pure mathematics, areas of applied mathematics, particularly PDEs, remain underexplored despite their significant real-world applications. We present PDE-Controller, a framework that enables large language models (LLMs) to control systems governed by partial differential equations (PDEs). Our approach enables LLMs to transform informal natural language instructions into formal specifications, and then execute reasoning and planning steps to improve the utility of PDE control. We build a holistic solution comprising datasets (both human-written cases and 2 million synthetic samples), math-reasoning models, and novel evaluation metrics, all of which require significant effort. Our PDE-Controller significantly outperforms prompting the latest open-source and GPT models in reasoning, autoformalization, and program synthesis, achieving up to a 62% improvement in utility gain for PDE control. By bridging the gap between language generation and PDE systems, we demonstrate the potential of LLMs in addressing complex scientific and engineering challenges. We will release all data, model checkpoints, and code at https://pde-controller.github.io/.

As current training data for Large Language Models (LLMs) are dominated by English corpus, they are English-centric and they present impressive performance on English reasoning tasks.This paper primarily studies English-centric models, but our method could be universal by using the centric language in the dictionary for non-English-centric LLMs. Yet, they usually suffer from lower performance in other languages. There are about 7,000 languages over the world, and many are low-resourced on English-centric LLMs. For the sake of people who primarily speak these languages, it is especially urgent to enable our LLMs in those languages. Model training is usually effective, but computationally expensive and requires experienced NLP practitioners. This paper presents a novel and simple yet effective method called Dictionary Insertion Prompting (DIP). When providing a non-English prompt, DIP looks up a word dictionary and inserts words' English counterparts into the prompt for LLMs. It then enables better translation into English and better English model thinking steps which leads to obviously better results. We experiment with about 200 languages from FLORES-200. Since there are no adequate datasets, we use the NLLB translator to create synthetic multilingual benchmarks from the existing 4 English reasoning benchmarks such as GSM8K and AQuA. Despite the simplicity and computationally lightweight, we surprisingly found the effectiveness of DIP on math and commonsense reasoning tasks on multiple open-source and close-source LLMs.Our dictionaries, code, and synthetic benchmarks will be open-sourced to facilitate future research.

Large language models (LLMs) have achieved substantial progress in processing long contexts but still struggle with long-context reasoning. Existing approaches typically involve fine-tuning LLMs with synthetic data, which depends on annotations from human experts or advanced models like GPT-4, thus restricting further advancements. To address this issue, we investigate the potential for LLMs to self-improve in long-context reasoning and propose \ours, an approach specifically designed for this purpose. This approach is straightforward: we sample multiple outputs for each question, score them with Minimum Bayes Risk, and then apply supervised fine-tuning or preference optimization based on these outputs. Extensive experiments on several leading LLMs demonstrate the effectiveness of \ours, with an absolute improvement of 4.2 points for Llama-3.1-8B-Instruct. Furthermore, \ours achieves superior performance compared to prior approaches that depend on data produced by human experts or advanced models. We anticipate that this work will open new avenues for self-improvement techniques in long-context scenarios, which are essential for the continual advancement of LLMs.

The utility of synthetic data to enhance pretraining data quality and hence to improve downstream task accuracy has been widely explored in recent large language models (LLMs). Yet, these approaches fall inadequate in complex, multi-hop and mathematical reasoning tasks as the synthetic data typically fails to add complementary knowledge to the existing raw corpus. In this work, we propose a novel large-scale and diverse Math Informed syNthetic Dialogue (MIND) generation method that improves the mathematical reasoning ability of LLMs. Specifically, using MIND, we generate synthetic conversations based on OpenWebMath (OWM), resulting in a new math corpus, MIND-OWM. Our experiments with different conversational settings reveal that incorporating knowledge gaps between dialog participants is essential for generating high-quality math data. We further identify an effective way to format and integrate synthetic and raw data during pretraining to maximize the gain in mathematical reasoning, emphasizing the need to restructure raw data rather than use it as-is. Compared to pretraining just on raw data, a model pretrained on MIND-OWM shows significant boost in mathematical reasoning (GSM8K: +13.42%, MATH: +2.30%), including superior performance in specialized knowledge (MMLU: +4.55%, MMLU-STEM: +4.28%) and general purpose reasoning tasks (GENERAL REASONING: +2.51%).

Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of LLMs, which inherently lacks mechanisms for differentiating between desirable and undesirable results. Drawing inspiration from the dual-process theory of human cognition, we introduce LLM2, a novel framework that combines an LLM (System 1) with a process-based verifier (System 2). Within LLM2, the LLM is responsible for generating plausible candidates, while the verifier provides timely process-based feedback to distinguish desirable and undesirable outputs. The verifier is trained with a pairwise comparison loss on synthetic process-supervision data generated through our token quality exploration strategy. Empirical results on mathematical reasoning benchmarks substantiate the efficacy of LLM2, exemplified by an accuracy enhancement from 50.3 to 57.8 (+7.5) for Llama3-1B on GSM8K. Furthermore, when combined with self-consistency, LLM2 achieves additional improvements, boosting major@20 accuracy from 56.2 to 70.2 (+14.0).

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

Large language models (LLMs) have achieved remarkable performance in recent years but are fundamentally limited by the underlying training data. To improve models beyond the training data, recent works have explored how LLMs can be used to generate synthetic data for autonomous self-improvement. However, successive steps of self-improvement can reach a point of diminishing returns. In this work, we propose a complementary approach towards self-improvement where finetuning is applied to a multiagent society of language models. A group of language models, all starting from the same base model, are independently specialized by updating each one using data generated through multiagent interactions among the models. By training each model on independent sets of data, we illustrate how this approach enables specialization across models and diversification over the set of models. As a result, our overall system is able to preserve diverse reasoning chains and autonomously improve over many more rounds of fine-tuning than single-agent self-improvement methods. We quantitatively illustrate the efficacy of the approach across a wide suite of reasoning tasks.

Weird, unusual, and uncanny images pique the curiosity of observers because they challenge commonsense. For example, an image released during the 2022 world cup depicts the famous soccer stars Lionel Messi and Cristiano Ronaldo playing chess, which playfully violates our expectation that their competition should occur on the football field. Humans can easily recognize and interpret these unconventional images, but can AI models do the same? We introduce WHOOPS!, a new dataset and benchmark for visual commonsense. The dataset is comprised of purposefully commonsense-defying images created by designers using publicly-available image generation tools like Midjourney. We consider several tasks posed over the dataset. In addition to image captioning, cross-modal matching, and visual question answering, we introduce a difficult explanation generation task, where models must identify and explain why a given image is unusual. Our results show that state-of-the-art models such as GPT3 and BLIP2 still lag behind human performance on WHOOPS!. We hope our dataset will inspire the development of AI models with stronger visual commonsense reasoning abilities. Data, models and code are available at the project website: whoops-benchmark.github.io

Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning abilities, i.e., the ability to decompose complex questions into step-by-step reasoning chains, but such ability seems only to emerge from models with abundant parameters. This work investigates how to incorporate relatively small LMs with the capabilities of multi-step reasoning. We propose to inject such abilities by continually pre-training LMs on a synthetic dataset MsAT which is composed of Multi-step Arithmetic Tasks. Our experiments on four math word problem datasets show the effectiveness of the proposed method in enhancing LMs' math reasoning abilities.

Physical reasoning, which involves the interpretation, understanding, and prediction of object behavior in dynamic environments, remains a significant challenge for current Vision-Language Models (VLMs). In this work, we propose two methods to enhance VLMs' physical reasoning capabilities using simulated data. First, we fine-tune a pre-trained VLM using question-answer (QA) pairs generated from simulations relevant to physical reasoning tasks. Second, we introduce Physics Context Builders (PCBs), specialized VLMs fine-tuned to create scene descriptions enriched with physical properties and processes. During physical reasoning tasks, these PCBs can be leveraged as context to assist a Large Language Model (LLM) to improve its performance. We evaluate both of our approaches using multiple benchmarks, including a new stability detection QA dataset called Falling Tower, which includes both simulated and real-world scenes, and CLEVRER. We demonstrate that a small QA fine-tuned VLM can significantly outperform larger state-of-the-art foundational models. We also show that integrating PCBs boosts the performance of foundational LLMs on physical reasoning tasks. Using the real-world scenes from the Falling Tower dataset, we also validate the robustness of both approaches in Sim2Real transfer. Our results highlight the utility that simulated data can have in the creation of learning systems capable of advanced physical reasoning.

Code has been shown to be effective in enhancing the mathematical reasoning abilities of large language models due to its precision and accuracy. Previous works involving continued mathematical pretraining often include code that utilizes math-related packages, which are primarily designed for fields such as engineering, machine learning, signal processing, or module testing, rather than being directly focused on mathematical reasoning. In this paper, we introduce a novel method for generating mathematical code accompanied with corresponding reasoning steps for continued pretraining. Our approach begins with the construction of a high-quality mathematical continued pretraining dataset by incorporating math-related web data, code using mathematical packages, math textbooks, and synthetic data. Next, we construct reasoning steps by extracting LaTeX expressions, the conditions needed for the expressions, and the results of the expressions from the previously collected dataset. Based on this extracted information, we generate corresponding code to accurately capture the mathematical reasoning process. Appending the generated code to each reasoning step results in data consisting of paired natural language reasoning steps and their corresponding code. Combining this data with the original dataset results in a 19.2B-token high-performing mathematical pretraining corpus, which we name MathCode-Pile. Training several popular base models with this corpus significantly improves their mathematical abilities, leading to the creation of the MathCoder2 family of models. All of our data processing and training code is open-sourced, ensuring full transparency and easy reproducibility of the entire data collection and training pipeline. The code is released at https://github.com/mathllm/MathCoder2 .

Recent advancements in Large Vision-Language Models (LVLMs) have enabled processing of multimodal inputs in language models but require significant computational resources for deployment, especially in edge devices. This study aims to bridge the performance gap between traditional-scale LVLMs and resource-friendly lite versions by adopting high-quality training data. To do this, a synthetic dataset is created by leveraging GPT-4V's ability to generate detailed captions, complex reasoning instructions and detailed answers from images. The resulted model trained with our data, ALLaVA, achieves competitive performance on 12 benchmarks up to 3B LVLMs. This work highlights the feasibility of adopting high-quality data in crafting more efficient LVLMs. Our online demo is available at https://allava.freedomai.cn.

Vision-language models (VLMs), such as CLIP and ALIGN, are generally trained on datasets consisting of image-caption pairs obtained from the web. However, real-world multimodal datasets, such as healthcare data, are significantly more complex: each image (e.g. X-ray) is often paired with text (e.g. physician report) that describes many distinct attributes occurring in fine-grained regions of the image. We refer to these samples as exhibiting high pairwise complexity, since each image-text pair can be decomposed into a large number of region-attribute pairings. The extent to which VLMs can capture fine-grained relationships between image regions and textual attributes when trained on such data has not been previously evaluated. The first key contribution of this work is to demonstrate through systematic evaluations that as the pairwise complexity of the training dataset increases, standard VLMs struggle to learn region-attribute relationships, exhibiting performance degradations of up to 37% on retrieval tasks. In order to address this issue, we introduce ViLLA as our second key contribution. ViLLA, which is trained to capture fine-grained region-attribute relationships from complex datasets, involves two components: (a) a lightweight, self-supervised mapping model to decompose image-text samples into region-attribute pairs, and (b) a contrastive VLM to learn representations from generated region-attribute pairs. We demonstrate with experiments across four domains (synthetic, product, medical, and natural images) that ViLLA outperforms comparable VLMs on fine-grained reasoning tasks, such as zero-shot object detection (up to 3.6 AP50 points on COCO and 0.6 mAP points on LVIS) and retrieval (up to 14.2 R-Precision points).

Mathematics has long been conveyed through natural language, primarily for human understanding. With the rise of mechanized mathematics and proof assistants, there is a growing need to understand informal mathematical text, yet most existing benchmarks focus solely on English, overlooking other languages. This paper introduces RoMath, a Romanian mathematical reasoning benchmark suite comprising three datasets: RoMath-Baccalaureate, RoMath-Competitions and RoMath-Synthetic, which cover a range of mathematical domains and difficulty levels, aiming to improve non-English language models and promote multilingual AI development. By focusing on Romanian, a low-resource language with unique linguistic features, RoMath addresses the limitations of Anglo-centric models and emphasizes the need for dedicated resources beyond simple automatic translation. We benchmark several open-weight language models, highlighting the importance of creating resources for underrepresented languages. We make the code and dataset available.

We introduce OmnixR, an evaluation suite designed to benchmark SoTA Omni-modality Language Models, such as GPT-4o and Gemini. Evaluating OLMs, which integrate multiple modalities such as text, vision, and audio, presents unique challenges. Particularly, the user message might often consist of multiple modalities, such that OLMs have to establish holistic understanding and reasoning across modalities to accomplish the task. Existing benchmarks are limited to single modality or dual-modality tasks, overlooking comprehensive multi-modal assessments of model reasoning. To address this, OmnixR offers two evaluation variants: (1)synthetic subset: a synthetic dataset generated automatically by translating text into multiple modalities--audio, images, video, and hybrids (Omnify). (2)realistic subset: a real-world dataset, manually curated and annotated by experts, for evaluating cross-modal reasoning in natural settings. OmnixR presents a unique evaluation towards assessing OLMs over a diverse mix of modalities, such as a question that involves video, audio, and text, providing a rigorous cross-modal reasoning testbed unlike any existing benchmarks. Our experiments find that all state-of-the-art OLMs struggle with OmnixR questions that require integrating information from multiple modalities to answer. Further analysis highlights differences in reasoning behavior, underscoring the challenges of omni-modal AI alignment.

We propose a novel framework, Meta Chain-of-Thought (Meta-CoT), which extends traditional Chain-of-Thought (CoT) by explicitly modeling the underlying reasoning required to arrive at a particular CoT. We present empirical evidence from state-of-the-art models exhibiting behaviors consistent with in-context search, and explore methods for producing Meta-CoT via process supervision, synthetic data generation, and search algorithms. Finally, we outline a concrete pipeline for training a model to produce Meta-CoTs, incorporating instruction tuning with linearized search traces and reinforcement learning post-training. Finally, we discuss open research questions, including scaling laws, verifier roles, and the potential for discovering novel reasoning algorithms. This work provides a theoretical and practical roadmap to enable Meta-CoT in LLMs, paving the way for more powerful and human-like reasoning in artificial intelligence.

Understanding and reasoning over non-speech sounds and music are crucial for both humans and AI agents to interact effectively with their environments. In this paper, we introduce Audio Flamingo 2 (AF2), an Audio-Language Model (ALM) with advanced audio understanding and reasoning capabilities. AF2 leverages (i) a custom CLAP model, (ii) synthetic Audio QA data for fine-grained audio reasoning, and (iii) a multi-stage curriculum learning strategy. AF2 achieves state-of-the-art performance with only a 3B parameter small language model, surpassing large open-source and proprietary models across over 20 benchmarks. Next, for the first time, we extend audio understanding to long audio segments (30 secs to 5 mins) and propose LongAudio, a large and novel dataset for training ALMs on long audio captioning and question-answering tasks. Fine-tuning AF2 on LongAudio leads to exceptional performance on our proposed LongAudioBench, an expert annotated benchmark for evaluating ALMs on long audio understanding capabilities. We conduct extensive ablation studies to confirm the efficacy of our approach. Project Website: https://research.nvidia.com/labs/adlr/AF2/.

Prior research on training grounded factuality classification models to detect hallucinations in large language models (LLMs) has relied on public natural language inference (NLI) data and synthetic data. However, conventional NLI datasets are not well-suited for document-level reasoning, which is critical for detecting LLM hallucinations. Recent approaches to document-level synthetic data generation involve iteratively removing sentences from documents and annotating factuality using LLM-based prompts. While effective, this method is computationally expensive for long documents and limited by the LLM's capabilities. In this work, we analyze the differences between existing synthetic training data used in state-of-the-art models and real LLM output claims. Based on our findings, we propose a novel approach for synthetic data generation, CG2C, that leverages multi-hop reasoning on context graphs extracted from documents. Our fact checker model, FactCG, demonstrates improved performance with more connected reasoning, using the same backbone models. Experiments show it even outperforms GPT-4-o on the LLM-Aggrefact benchmark with much smaller model size.

Scaling laws in language modeling traditionally quantify training loss as a function of dataset size and model parameters, providing compute-optimal estimates but often neglecting the impact of data quality on model generalization. In this paper, we extend the conventional understanding of scaling law by offering a microscopic view of data quality within the original formulation -- effective training tokens -- which we posit to be a critical determinant of performance for parameter-constrained language models. Specifically, we formulate the proposed term of effective training tokens to be a combination of two readily-computed indicators of text: (i) text diversity and (ii) syntheticity as measured by a teacher model. We pretrained over 200 models of 25M to 1.5B parameters on a diverse set of sampled, synthetic data, and estimated the constants that relate text quality, model size, training tokens, and eight reasoning task accuracy scores. We demonstrated the estimated constants yield +0.83 Pearson correlation with true accuracies, and analyzed it in scenarios involving widely-used data techniques such as data sampling and synthesis which aim to improve data quality.

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations (or ``chain-of-thought'' (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for symbolic programming. To make progress towards understanding in-context learning, we curate synthetic datasets containing equivalent (natural, symbolic) data pairs, where symbolic examples contain first-order logic rules and predicates from knowledge bases (KBs). Then we revisit neuro-symbolic approaches and use Language Models as Logic Programmer (LMLP) that learns from demonstrations containing logic rules and corresponding examples to iteratively reason over KBs, recovering Prolog's backward chaining algorithm. Comprehensive experiments are included to systematically compare LMLP with CoT in deductive reasoning settings, showing that LMLP enjoys more than 25% higher accuracy than CoT on length generalization benchmarks even with fewer parameters.

Large language models (LLMs) have showcased remarkable reasoning capabilities, yet they remain susceptible to errors, particularly in temporal reasoning tasks involving complex temporal logic. Existing research has explored LLM performance on temporal reasoning using diverse datasets and benchmarks. However, these studies often rely on real-world data that LLMs may have encountered during pre-training or employ anonymization techniques that can inadvertently introduce factual inconsistencies. In this work, we address these limitations by introducing novel synthetic datasets specifically designed to assess LLM temporal reasoning abilities in various scenarios. The diversity of question types across these datasets enables systematic investigation into the impact of the problem structure, size, question type, fact order, and other factors on LLM performance. Our findings provide valuable insights into the strengths and weaknesses of current LLMs in temporal reasoning tasks. To foster further research in this area, we are open-sourcing the datasets and evaluation framework used in our experiments: https://huggingface.co/datasets/baharef/ToT.

Vision-language models (VLMs) have shown impressive zero- and few-shot performance on real-world visual question answering (VQA) benchmarks, alluding to their capabilities as visual reasoning engines. However, the benchmarks being used conflate "pure" visual reasoning with world knowledge, and also have questions that involve a limited number of reasoning steps. Thus, it remains unclear whether a VLM's apparent visual reasoning performance is due to its world knowledge, or due to actual visual reasoning capabilities. To clarify this ambiguity, we systematically benchmark and dissect the zero-shot visual reasoning capabilities of VLMs through synthetic datasets that require minimal world knowledge, and allow for analysis over a broad range of reasoning steps. We focus on two novel aspects of zero-shot visual reasoning: i) evaluating the impact of conveying scene information as either visual embeddings or purely textual scene descriptions to the underlying large language model (LLM) of the VLM, and ii) comparing the effectiveness of chain-of-thought prompting to standard prompting for zero-shot visual reasoning. We find that the underlying LLMs, when provided textual scene descriptions, consistently perform better compared to being provided visual embeddings. In particular, 18% higher accuracy is achieved on the PTR dataset. We also find that CoT prompting performs marginally better than standard prompting only for the comparatively large GPT-3.5-Turbo (175B) model, and does worse for smaller-scale models. This suggests the emergence of CoT abilities for visual reasoning in LLMs at larger scales even when world knowledge is limited. Overall, we find limitations in the abilities of VLMs and LLMs for more complex visual reasoning, and highlight the important role that LLMs can play in visual reasoning.

Large language models (LLMs) have demonstrated impressive capabilities in mathematical problem solving, particularly in single turn question answering formats. However, real world scenarios often involve mathematical question answering that requires multi turn or interactive information exchanges, and the performance of LLMs on these tasks is still underexplored. This paper introduces MathChat, a comprehensive benchmark specifically designed to evaluate LLMs across a broader spectrum of mathematical tasks. These tasks are structured to assess the models' abilities in multiturn interactions and open ended generation. We evaluate the performance of various SOTA LLMs on the MathChat benchmark, and we observe that while these models excel in single turn question answering, they significantly underperform in more complex scenarios that require sustained reasoning and dialogue understanding. To address the above limitations of existing LLMs when faced with multiturn and open ended tasks, we develop MathChat sync, a synthetic dialogue based math dataset for LLM finetuning, focusing on improving models' interaction and instruction following capabilities in conversations. Experimental results emphasize the need for training LLMs with diverse, conversational instruction tuning datasets like MathChatsync. We believe this work outlines one promising direction for improving the multiturn mathematical reasoning abilities of LLMs, thus pushing forward the development of LLMs that are more adept at interactive mathematical problem solving and real world applications.

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify when and where to refine without access to external feedback. Outcome-based Reward Models (ORMs), trained to predict correctness of the final answer indicating when to refine, offer one convenient solution for deciding when to refine. Process Based Reward Models (PRMs), trained to predict correctness of intermediate steps, can then be used to indicate where to refine. But they are expensive to train, requiring extensive human annotations. In this paper, we propose Stepwise ORMs (SORMs) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or V^{star}. More specifically, SORMs are trained to predict the correctness of the final answer when sampling the current policy many times (rather than only once as in the case of ORMs). Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus improving downstream accuracy when doing refinements. We then train global refinement models, which take only the question and a draft solution as input and predict a corrected solution, and local refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53\% to 65\% when greedily sampled.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Vision language models (VLMs) have demonstrated impressive performance across a wide range of downstream tasks. However, their proficiency in spatial reasoning remains limited, despite its crucial role in tasks involving navigation and interaction with physical environments. Specifically, most of these tasks rely on the core spatial reasoning capabilities in two-dimensional (2D) environments, and our evaluation reveals that state-of-the-art VLMs frequently generate implausible and incorrect responses to composite spatial reasoning problems, including simple pathfinding tasks that humans can solve effortlessly at a glance. To address this, we explore an effective approach to enhance 2D spatial reasoning within VLMs by training the model solely on basic spatial capabilities. We begin by disentangling the key components of 2D spatial reasoning: direction comprehension, distance estimation, and localization. Our central hypothesis is that mastering these basic spatial capabilities can significantly enhance a model's performance on composite spatial tasks requiring advanced spatial understanding and combinatorial problem-solving, with generalized improvements in visual-spatial tasks. To investigate this hypothesis, we introduce Sparkle, a framework that fine-tunes VLMs on these three basic spatial capabilities by synthetic data generation and targeted supervision to form an instruction dataset for each capability. Our experiments demonstrate that VLMs fine-tuned with Sparkle achieve significant performance gains, not only in the basic tasks themselves but also in generalizing to composite and out-of-distribution spatial reasoning tasks. These findings underscore the effectiveness of mastering basic spatial capabilities in enhancing composite spatial problem-solving, offering insights into systematic strategies for improving VLMs' spatial reasoning capabilities.

Training on high-quality synthetic data from strong language models (LMs) is a common strategy to improve the reasoning performance of LMs. In this work, we revisit whether this strategy is compute-optimal under a fixed inference budget (e.g., FLOPs). To do so, we investigate the trade-offs between generating synthetic data using a stronger but more expensive (SE) model versus a weaker but cheaper (WC) model. We evaluate the generated data across three key metrics: coverage, diversity, and false positive rate, and show that the data from WC models may have higher coverage and diversity, but also exhibit higher false positive rates. We then finetune LMs on data from SE and WC models in different settings: knowledge distillation, self-improvement, and a novel weak-to-strong improvement setup where a weaker LM teaches reasoning to a stronger LM. Our findings reveal that models finetuned on WC-generated data consistently outperform those trained on SE-generated data across multiple benchmarks and multiple choices of WC and SE models. These results challenge the prevailing practice of relying on SE models for synthetic data generation, suggesting that WC may be the compute-optimal approach for training advanced LM reasoners.

Vision-Language Models (VLMs) excel at identifying and describing objects but struggle with spatial reasoning such as accurately understanding the relative positions of objects. Inspired by the dual-pathway (ventral-dorsal) model of human vision, we investigate why VLMs fail spatial tasks despite strong object recognition capabilities. Our interpretability-driven analysis reveals a critical underlying cause: vision embeddings in VLMs are treated primarily as semantic ``bag-of-tokens," overshadowing subtle yet crucial positional cues due to their disproportionately large embedding norms. We validate this insight through extensive diagnostic experiments, demonstrating minimal performance impact when token orders or fine-grained spatial details are removed. Guided by these findings, we propose simple, interpretable interventions, including normalizing vision embedding norms and extracting mid-layer spatially rich features, to restore spatial awareness. Empirical results on both our synthetic data and standard benchmarks demonstrate improved spatial reasoning capabilities, highlighting the value of interpretability-informed design choices. Our study not only uncovers fundamental limitations in current VLM architectures but also provides actionable insights for enhancing structured perception of visual scenes.

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning accuracy, particularly by using pretrained language models to "self-correct" their mistakes via multi-round prompting. In this paper, we follow this line of work but focus on understanding the usefulness of incorporating "error-correction" data directly into the pretraining stage. This data consists of erroneous solution steps immediately followed by their corrections. Using a synthetic math dataset, we show promising results: this type of pretrain data can help language models achieve higher reasoning accuracy directly (i.e., through simple auto-regression, without multi-round prompting) compared to pretraining on the same amount of error-free data. We also delve into many details, such as (1) how this approach differs from beam search, (2) how such data can be prepared, (3) whether masking is needed on the erroneous tokens, (4) the amount of error required, (5) whether such data can be deferred to the fine-tuning stage, and many others.

Statistical shape modeling (SSM) enables population-based quantitative analysis of anatomical shapes, informing clinical diagnosis. Deep learning approaches predict correspondence-based SSM directly from unsegmented 3D images but require calibrated uncertainty quantification, motivating Bayesian formulations. Variational information bottleneck DeepSSM (VIB-DeepSSM) is an effective, principled framework for predicting probabilistic shapes of anatomy from images with aleatoric uncertainty quantification. However, VIB is only half-Bayesian and lacks epistemic uncertainty inference. We derive a fully Bayesian VIB formulation and demonstrate the efficacy of two scalable implementation approaches: concrete dropout and batch ensemble. Additionally, we introduce a novel combination of the two that further enhances uncertainty calibration via multimodal marginalization. Experiments on synthetic shapes and left atrium data demonstrate that the fully Bayesian VIB network predicts SSM from images with improved uncertainty reasoning without sacrificing accuracy.

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level modifications-such as rephrasing or generating syntactic variations-which fail to capture and leverage the intrinsic relational structures inherent in mathematical knowledge. Inspired by human learning processes, where mathematical proficiency develops through systematic exposure to interconnected concepts, we introduce MathFusion, a novel framework that enhances mathematical reasoning through cross-problem instruction synthesis. MathFusion implements this through three fusion strategies: (1) sequential fusion, which chains related problems to model solution dependencies; (2) parallel fusion, which combines analogous problems to reinforce conceptual understanding; and (3) conditional fusion, which creates context-aware selective problems to enhance reasoning flexibility. By applying these strategies, we generate a new dataset, MathFusionQA, followed by fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental results demonstrate that MathFusion achieves substantial improvements in mathematical reasoning while maintaining high data efficiency, boosting performance by 18.0 points in accuracy across diverse benchmarks while requiring only 45K additional synthetic instructions, representing a substantial improvement over traditional single-instruction approaches. Our datasets, models, and code are publicly available at https://github.com/QizhiPei/mathfusion.

Advanced AI assistants combine frontier LLMs and tool access to autonomously perform complex tasks on behalf of users. While the helpfulness of such assistants can increase dramatically with access to user information including emails and documents, this raises privacy concerns about assistants sharing inappropriate information with third parties without user supervision. To steer information-sharing assistants to behave in accordance with privacy expectations, we propose to operationalize contextual integrity (CI), a framework that equates privacy with the appropriate flow of information in a given context. In particular, we design and evaluate a number of strategies to steer assistants' information-sharing actions to be CI compliant. Our evaluation is based on a novel form filling benchmark composed of synthetic data and human annotations, and it reveals that prompting frontier LLMs to perform CI-based reasoning yields strong results.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Large Language Models (LLMs) have significantly advanced various fields, particularly coding, mathematical reasoning, and logical problem solving. However, a critical question remains: Do these mathematical reasoning abilities persist when LLMs are presented with culturally adapted math problems? Specifically, how do LLMs perform when faced with math problems embedded in cultural contexts that have no significant representation in main stream web-scale AI training data? To explore this, we generated six synthetic cultural datasets from GSM8K, a widely used benchmark for assessing LLMs' mathematical reasoning skills. While preserving the mathematical logic and numerical values of the original GSM8K test set, we modify cultural elements such as personal names, food items, place names, etc. These culturally adapted datasets provide a more reliable framework for evaluating LLMs' mathematical reasoning under shifting cultural contexts. Our findings reveal that LLMs struggle with math problems when cultural references change, even though the underlying mathematical structure remains constant. Smaller models exhibit greater performance drops compared to larger models. Interestingly, our results also suggest that cultural familiarity can enhance mathematical reasoning. Even models with no explicit mathematical training but exposure to relevant cultural contexts sometimes outperform larger, mathematically proficient models on culturally embedded math problems. This study highlights the impact of cultural context on the mathematical reasoning abilities of LLMs, underscoring the need for more diverse and representative training data to improve robustness in real-world applications. The benchmark data sets and script for reproducing the results are available at https://github.com/akarim23131/Lost_in_Cultural_Translation

Neural Machine Translation (NMT) driven by Transformer architectures has advanced significantly, yet faces challenges with low-resource language pairs like Vietnamese-Japanese (Vi-Ja). Issues include sparse parallel data and handling linguistic/cultural nuances. Recent progress in Large Language Models (LLMs) with strong reasoning, often refined via Reinforcement Learning (RL), enables high-quality synthetic data generation. We introduce VNJPTranslate, a pipeline designed to systematically address the Vi-Ja translation task. It features a targeted data augmentation strategy using advanced LLMs with Chain-of-Thought prompting for challenging segments identified via corpus analysis. Subsequently, we employ efficient fine-tuning techniques (Unsloth with QLoRA) on a capable, low-parameter autoregressive model (specifically, a fine-tuned version of the 1.8B parameter Sailor model, which is based on the Qwen architecture) to create a practical and high-performing translation system. This integrated approach aims to improve Vi-Ja translation quality significantly over existing baselines.

Mastering commonsense understanding and reasoning is a pivotal skill essential for conducting engaging conversations. While there have been several attempts to create datasets that facilitate commonsense inferences in dialogue contexts, existing datasets tend to lack in-depth details, restate information already present in the conversation, and often fail to capture the multifaceted nature of commonsense reasoning. In response to these limitations, we compile a new synthetic dataset for commonsense reasoning in dialogue contexts using GPT, ConvoSense, that boasts greater contextual novelty, offers a higher volume of inferences per example, and substantially enriches the detail conveyed by the inferences. Our dataset contains over 500,000 inferences across 12,000 dialogues with 10 popular inference types, which empowers the training of generative commonsense models for dialogue that are superior in producing plausible inferences with high novelty when compared to models trained on the previous datasets. To the best of our knowledge, ConvoSense is the first of its kind to provide such a multitude of novel inferences at such a large scale.

Despite recent progress in improving the mathematical reasoning ability of large language models(LLMs), solving competition-level math problems without the use of external tools remains challenging for open-source LLMs. In this work, we introduce the MMIQC dataset, a mixture of processed web data and synthetic question-response pairs, to equip base models with better mathematical reasoning skills. Mistral-7B-MMIQC, the model obtained by fine-tuning Mistral-7B(arXiv:2310.06825) on MMIQC, achieves 36.0\% accuracy on MATH(arXiv:2103.03874), 5.8\% higher than the previous (model size sim7B) SOTA. Our experiments also show that a large part of the improvement attributes to our novel augmentation method IQC(Iterative Question Composing), where we iteratively ask an LLM to compose new questions from the given seed problems and do rejection sampling from another LLM. MMIQC has now been released on https://huggingface.co/datasets/Vivacem/MMIQC.

While diffusion models are powerful in generating high-quality, diverse synthetic data for object-centric tasks, existing methods struggle with scene-aware tasks such as Visual Question Answering (VQA) and Human-Object Interaction (HOI) Reasoning, where it is critical to preserve scene attributes in generated images consistent with a multimodal context, i.e. a reference image with accompanying text guidance query. To address this, we introduce Hummingbird, the first diffusion-based image generator which, given a multimodal context, generates highly diverse images w.r.t. the reference image while ensuring high fidelity by accurately preserving scene attributes, such as object interactions and spatial relationships from the text guidance. Hummingbird employs a novel Multimodal Context Evaluator that simultaneously optimizes our formulated Global Semantic and Fine-grained Consistency Rewards to ensure generated images preserve the scene attributes of reference images in relation to the text guidance while maintaining diversity. As the first model to address the task of maintaining both diversity and fidelity given a multimodal context, we introduce a new benchmark formulation incorporating MME Perception and Bongard HOI datasets. Benchmark experiments show Hummingbird outperforms all existing methods by achieving superior fidelity while maintaining diversity, validating Hummingbird's potential as a robust multimodal context-aligned image generator in complex visual tasks.

A long-term goal of machine learning is to build intelligent conversational agents. One recent popular approach is to train end-to-end models on a large amount of real dialog transcripts between humans (Sordoni et al., 2015; Vinyals & Le, 2015; Shang et al., 2015). However, this approach leaves many questions unanswered as an understanding of the precise successes and shortcomings of each model is hard to assess. A contrasting recent proposal are the bAbI tasks (Weston et al., 2015b) which are synthetic data that measure the ability of learning machines at various reasoning tasks over toy language. Unfortunately, those tests are very small and hence may encourage methods that do not scale. In this work, we propose a suite of new tasks of a much larger scale that attempt to bridge the gap between the two regimes. Choosing the domain of movies, we provide tasks that test the ability of models to answer factual questions (utilizing OMDB), provide personalization (utilizing MovieLens), carry short conversations about the two, and finally to perform on natural dialogs from Reddit. We provide a dataset covering 75k movie entities and with 3.5M training examples. We present results of various models on these tasks, and evaluate their performance.

Continual pre-training (CPT) has been an important approach for adapting language models to specific domains or tasks. To make the CPT approach more traceable, this paper presents a technical report for continually pre-training Llama-3 (8B), which significantly enhances the Chinese language ability and scientific reasoning ability of the backbone model. To enhance the new abilities while retaining the original abilities, we design specific data mixture and curriculum strategies by utilizing existing datasets and synthesizing high-quality datasets. Specifically, we synthesize multidisciplinary scientific question and answer (QA) pairs based on related web pages, and subsequently incorporate these synthetic data to improve the scientific reasoning ability of Llama-3. We refer to the model after CPT as Llama-3-SynE (Synthetic data Enhanced Llama-3). We also present the tuning experiments with a relatively small model -- TinyLlama, and employ the derived findings to train the backbone model. Extensive experiments on a number of evaluation benchmarks show that our approach can largely improve the performance of the backbone models, including both the general abilities (+8.81 on C-Eval and +6.31 on CMMLU) and the scientific reasoning abilities (+12.00 on MATH and +4.13 on SciEval), without hurting the original capacities. Our model, data, and codes are available at https://github.com/RUC-GSAI/Llama-3-SynE.

Answering complex questions that require making latent decisions is a challenging task, especially when limited supervision is available. Recent works leverage the capabilities of large language models (LMs) to perform complex question answering in a few-shot setting by demonstrating how to output intermediate rationalizations while solving the complex question in a single pass. We introduce ``Successive Prompting'', where we iteratively break down a complex task into a simple task, solve it, and then repeat the process until we get the final solution. Successive prompting decouples the supervision for decomposing complex questions from the supervision for answering simple questions, allowing us to (1) have multiple opportunities to query in-context examples at each reasoning step (2) learn question decomposition separately from question answering, including using synthetic data, and (3) use bespoke (fine-tuned) components for reasoning steps where a large LM does not perform well. The intermediate supervision is typically manually written, which can be expensive to collect. We introduce a way to generate a synthetic dataset which can be used to bootstrap a model's ability to decompose and answer intermediate questions. Our best model (with successive prompting) achieves an improvement of ~5% absolute F1 on a few-shot version of the DROP dataset when compared with a state-of-the-art model with the same supervision.

In this work we explore recent advances in instruction-tuning language models on a range of open instruction-following datasets. Despite recent claims that open models can be on par with state-of-the-art proprietary models, these claims are often accompanied by limited evaluation, making it difficult to compare models across the board and determine the utility of various resources. We provide a large set of instruction-tuned models from 6.7B to 65B parameters in size, trained on 12 instruction datasets ranging from manually curated (e.g., OpenAssistant) to synthetic and distilled (e.g., Alpaca) and systematically evaluate them on their factual knowledge, reasoning, multilinguality, coding, and open-ended instruction following abilities through a collection of automatic, model-based, and human-based metrics. We further introduce T\"ulu, our best performing instruction-tuned model suite finetuned on a combination of high-quality open resources. Our experiments show that different instruction-tuning datasets can uncover or enhance specific skills, while no single dataset (or combination) provides the best performance across all evaluations. Interestingly, we find that model and human preference-based evaluations fail to reflect differences in model capabilities exposed by benchmark-based evaluations, suggesting the need for the type of systemic evaluation performed in this work. Our evaluations show that the best model in any given evaluation reaches on average 83% of ChatGPT performance, and 68% of GPT-4 performance, suggesting that further investment in building better base models and instruction-tuning data is required to close the gap. We release our instruction-tuned models, including a fully finetuned 65B T\"ulu, along with our code, data, and evaluation framework at https://github.com/allenai/open-instruct to facilitate future research.

Difficult problems, which often result in long reasoning traces, are widely recognized as key factors for enhancing the performance of reasoning models. However, such high-challenge problems are scarce, limiting the size of available datasets. In this paper, we propose a simple method to decouple the reliance on problem difficulty. First, we empirically demonstrate that reasoning length, rather than problem difficulty, primarily influences the performance of trained models. Second, we identify a scaling law on reasoning length, showing that model performance increases in a log-linear fashion as the reasoning data length grows. Finally, we introduce a straightforward technique to generate reasoning data of arbitrary length, and show that synthesized data is effective for training reasoning models. After fine-tuning the Qwen2.5-32B-Instruct language model on our Long1K dataset, we present our model, Long1K-32B, which achieves remarkable performance with only 1,000 training samples, achieving 95.6\% accuracy on MATH, and 71.1\% on GPQA outperforming DeepSeek-R1-Distill-Qwen-32B. The model, code, and dataset are all open-sourced, available at https://huggingface.co/ZTss/LONG1.

Many methods now exist for conditioning model outputs on task instructions, retrieved documents, and user-provided explanations and feedback. Rather than relying solely on examples of task inputs and outputs, these approaches use valuable additional data for improving model correctness and aligning learned models with human priors. Meanwhile, a growing body of evidence suggests that some language models can (1) store a large amount of knowledge in their parameters, and (2) perform inference over tasks in textual inputs at test time. These results raise the possibility that, for some tasks, humans cannot explain to a model any more about the task than it already knows or could infer on its own. In this paper, we study the circumstances under which explanations of individual data points can (or cannot) improve modeling performance. In order to carefully control important properties of the data and explanations, we introduce a synthetic dataset for experiments, and we also make use of three existing datasets with explanations: e-SNLI, TACRED, and SemEval. We first give a formal framework for the available modeling approaches, in which explanation data can be used as model inputs, as targets, or as a prior. After arguing that the most promising role for explanation data is as model inputs, we propose to use a retrieval-based method and show that it solves our synthetic task with accuracies upwards of 95%, while baselines without explanation data achieve below 65% accuracy. We then identify properties of datasets for which retrieval-based modeling fails. With the three existing datasets, we find no improvements from explanation retrieval. Drawing on findings from our synthetic task, we suggest that at least one of six preconditions for successful modeling fails to hold with these datasets. Our code is publicly available at https://github.com/peterbhase/ExplanationRoles

Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or probabilistic) representation has been a major obstacle to this research. This paper investigates a modern approach to this problem where the facts and rules are provided as natural language sentences, thus bypassing a formal representation. We train transformers to reason (or emulate reasoning) over these sentences using synthetically generated data. Our models, that we call RuleTakers, provide the first empirical demonstration that this kind of soft reasoning over language is learnable, can achieve high (99%) accuracy, and generalizes to test data requiring substantially deeper chaining than seen during training (95%+ scores). We also demonstrate that the models transfer well to two hand-authored rulebases, and to rulebases paraphrased into more natural language. These findings are significant as it suggests a new role for transformers, namely as limited "soft theorem provers" operating over explicit theories in language. This in turn suggests new possibilities for explainability, correctability, and counterfactual reasoning in question-answering.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to the models, and creating many of them by hand is costly. We introduce Synthetic prompting, a method that leverages a few handcrafted examples to prompt the model to generate more examples by itself, and selects effective demonstrations to elicit better reasoning. Our method alternates between a backward and forward process to generate new examples. The backward process generates a question that match a sampled reasoning chain, so that the question is solvable and clear. The forward process produces a more detailed reasoning chain for the question, improving the quality of the example. We evaluate our method on numerical, symbolic, and algorithmic reasoning tasks, and show that it outperforms existing prompting techniques.

Recent progress in using machine learning models for reasoning tasks has been driven by novel model architectures, large-scale pre-training protocols, and dedicated reasoning datasets for fine-tuning. In this work, to further pursue these advances, we introduce a new data generator for machine reasoning that integrates with an embodied agent. The generated data consists of templated text queries and answers, matched with world-states encoded into a database. The world-states are a result of both world dynamics and the actions of the agent. We show the results of several baseline models on instantiations of train sets. These include pre-trained language models fine-tuned on a text-formatted representation of the database, and graph-structured Transformers operating on a knowledge-graph representation of the database. We find that these models can answer some questions about the world-state, but struggle with others. These results hint at new research directions in designing neural reasoning models and database representations. Code to generate the data will be released at github.com/facebookresearch/neuralmemory

While large language models (LLMs) equipped with techniques like chain-of-thought prompting have demonstrated impressive capabilities, they still fall short in their ability to reason robustly in complex settings. However, evaluating LLM reasoning is challenging because system capabilities continue to grow while benchmark datasets for tasks like logical deduction have remained static. We introduce MuSR, a dataset for evaluating language models on multistep soft reasoning tasks specified in a natural language narrative. This dataset has two crucial features. First, it is created through a novel neurosymbolic synthetic-to-natural generation algorithm, enabling the construction of complex reasoning instances that challenge GPT-4 (e.g., murder mysteries roughly 1000 words in length) and which can be scaled further as more capable LLMs are released. Second, our dataset instances are free text narratives corresponding to real-world domains of reasoning; this makes it simultaneously much more challenging than other synthetically-crafted benchmarks while remaining realistic and tractable for human annotators to solve with high accuracy. We evaluate a range of LLMs and prompting techniques on this dataset and characterize the gaps that remain for techniques like chain-of-thought to perform robust reasoning.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

We introduce Rank1, the first reranking model trained to take advantage of test-time compute. Rank1 demonstrates the applicability within retrieval of using a reasoning language model (i.e. OpenAI's o1, Deepseek's R1, etc.) for distillation in order to rapidly improve the performance of a smaller model. We gather and open-source a dataset of more than 600,000 examples of R1 reasoning traces from queries and passages in MS MARCO. Models trained on this dataset show: (1) state-of-the-art performance on advanced reasoning and instruction following datasets; (2) work remarkably well out of distribution due to the ability to respond to user-input prompts; and (3) have explainable reasoning chains that can be given to users or RAG-based systems. Further, we demonstrate that quantized versions of these models retain strong performance while using less compute/memory. Overall, Rank1 shows that test-time compute allows for a fundamentally new type of explainable and performant reranker model for search.

Large language models have demonstrated impressive capabilities across various natural language processing tasks, especially in solving mathematical problems. However, large language models are not good at math theorem proving using formal languages like Lean. A significant challenge in this area is the scarcity of training data available in these formal languages. To address this issue, we propose a novel pipeline that iteratively generates and filters synthetic data to translate natural language mathematical problems into Lean 4 statements, and vice versa. Our results indicate that the synthetic data pipeline can provide useful training data and improve the performance of LLMs in translating and understanding complex mathematical problems and proofs. Our final dataset contains about 57K formal-informal question pairs along with searched proof from the math contest forum and 21 new IMO questions. We open-source our code at https://github.com/InternLM/InternLM-Math and our data at https://huggingface.co/datasets/InternLM/Lean-Workbook.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Solving complex mathematical problems via system-2 reasoning is a natural human skill, yet it remains a significant challenge for current large language models (LLMs). We identify the scarcity of deliberate multi-step reasoning data as a primary limiting factor. To this end, we introduce Enriched Instruction Tuning (EIT), a method that enriches existing human-annotated mathematical datasets by synergizing human and AI feedback to create fine-grained reasoning trajectories. These datasets are then used to fine-tune open-source LLMs, enhancing their mathematical reasoning abilities without reliance on any symbolic verification program. Concretely, EIT is composed of two critical steps: Enriching with Reasoning Plan (ERP) and Enriching with Reasoning Step (ERS). The former generates a high-level plan that breaks down complex instructions into a sequence of simpler objectives, while ERS fills in reasoning contexts often overlooked by human annotators, creating a smoother reasoning trajectory for LLM fine-tuning. Unlike existing CoT prompting methods that generate reasoning chains only depending on LLM's internal knowledge, our method leverages human-annotated initial answers as ``meta-knowledge'' to help LLMs generate more detailed and precise reasoning processes, leading to a more trustworthy LLM expert for complex mathematical problems. In experiments, EIT achieves an accuracy of 84.1% on GSM8K and 32.5% on MATH, surpassing state-of-the-art fine-tuning and prompting methods, and even matching the performance of tool-augmented methods.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Large language models (LLMs) with memory are computationally universal. However, mainstream LLMs are not taking full advantage of memory, and the designs are heavily influenced by biological brains. Due to their approximate nature and proneness to the accumulation of errors, conventional neural memory mechanisms cannot support LLMs to simulate complex reasoning. In this paper, we seek inspiration from modern computer architectures to augment LLMs with symbolic memory for complex multi-hop reasoning. Such a symbolic memory framework is instantiated as an LLM and a set of SQL databases, where the LLM generates SQL instructions to manipulate the SQL databases. We validate the effectiveness of the proposed memory framework on a synthetic dataset requiring complex reasoning. The project website is available at https://chatdatabase.github.io/ .

We present a fundamental discovery that challenges our understanding of how complex reasoning emerges in large language models. While conventional wisdom suggests that sophisticated reasoning tasks demand extensive training data (>100,000 examples), we demonstrate that complex mathematical reasoning abilities can be effectively elicited with surprisingly few examples. Through comprehensive experiments, our proposed model LIMO demonstrates unprecedented performance in mathematical reasoning. With merely 817 curated training samples, LIMO achieves 57.1% accuracy on AIME and 94.8% on MATH, improving from previous SFT-based models' 6.5% and 59.2% respectively, while only using 1% of the training data required by previous approaches. LIMO demonstrates exceptional out-of-distribution generalization, achieving 40.5% absolute improvement across 10 diverse benchmarks, outperforming models trained on 100x more data, challenging the notion that SFT leads to memorization rather than generalization. Based on these results, we propose the Less-Is-More Reasoning Hypothesis (LIMO Hypothesis): In foundation models where domain knowledge has been comprehensively encoded during pre-training, sophisticated reasoning capabilities can emerge through minimal but precisely orchestrated demonstrations of cognitive processes. This hypothesis posits that the elicitation threshold for complex reasoning is determined by two key factors: (1) the completeness of the model's encoded knowledge foundation during pre-training, and (2) the effectiveness of post-training examples as "cognitive templates" that show the model how to utilize its knowledge base to solve complex reasoning tasks. To facilitate reproducibility and future research in data-efficient reasoning, we release LIMO as a comprehensive open-source suite at https://github.com/GAIR-NLP/LIMO.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

This paper takes a first step towards a critical thinking curriculum for neural auto-regressive language models. We introduce a synthetic corpus of deductively valid arguments, and generate artificial argumentative texts to train and evaluate GPT-2. Significant transfer learning effects can be observed: Training a model on three simple core schemes allows it to accurately complete conclusions of different, and more complex types of arguments, too. The language models generalize the core argument schemes in a correct way. Moreover, we obtain consistent and promising results for NLU benchmarks. In particular, pre-training on the argument schemes raises zero-shot accuracy on the GLUE diagnostics by up to 15 percentage points. The findings suggest that intermediary pre-training on texts that exemplify basic reasoning abilities (such as typically covered in critical thinking textbooks) might help language models to acquire a broad range of reasoning skills. The synthetic argumentative texts presented in this paper are a promising starting point for building such a "critical thinking curriculum for language models."

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Large Language Models (LLMs) have demonstrated impressive capabilities in natural language processing tasks, such as text generation and semantic understanding. However, their performance on numerical reasoning tasks, such as basic arithmetic, numerical retrieval, and magnitude comparison, remains surprisingly poor. This gap arises from their reliance on surface-level statistical patterns rather than understanding numbers as continuous magnitudes. Existing benchmarks primarily focus on either linguistic competence or structured mathematical problem-solving, neglecting fundamental numerical reasoning required in real-world scenarios. To bridge this gap, we propose NumericBench, a comprehensive benchmark to evaluate six fundamental numerical capabilities: number recognition, arithmetic operations, contextual retrieval, comparison, summary, and logical reasoning. NumericBench includes datasets ranging from synthetic number lists to the crawled real-world data, addressing challenges like long contexts, noise, and multi-step reasoning. Extensive experiments on state-of-the-art LLMs, including GPT-4 and DeepSeek, reveal persistent weaknesses in numerical reasoning, highlighting the urgent need to improve numerically-aware language modeling. The benchmark is released in: https://github.com/TreeAI-Lab/NumericBench.

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning domains like mathematics and programming by harnessing supervised fine-tuning (SFT) and reinforcement learning (RL) techniques to enhance the Chain-of-Thought (CoT) reasoning. However, while longer CoT reasoning sequences improve performance, they also introduce significant computational overhead due to verbose and redundant outputs, known as the "overthinking phenomenon". In this paper, we provide the first structured survey to systematically investigate and explore the current progress toward achieving efficient reasoning in LLMs. Overall, relying on the inherent mechanism of LLMs, we categorize existing works into several key directions: (1) model-based efficient reasoning, which considers optimizing full-length reasoning models into more concise reasoning models or directly training efficient reasoning models; (2) reasoning output-based efficient reasoning, which aims to dynamically reduce reasoning steps and length during inference; (3) input prompts-based efficient reasoning, which seeks to enhance reasoning efficiency based on input prompt properties such as difficulty or length control. Additionally, we introduce the use of efficient data for training reasoning models, explore the reasoning capabilities of small language models, and discuss evaluation methods and benchmarking.

We introduce Phi-4-Mini and Phi-4-Multimodal, compact yet highly capable language and multimodal models. Phi-4-Mini is a 3.8-billion-parameter language model trained on high-quality web and synthetic data, significantly outperforming recent open-source models of similar size and matching the performance of models twice its size on math and coding tasks requiring complex reasoning. This achievement is driven by a carefully curated synthetic data recipe emphasizing high-quality math and coding datasets. Compared to its predecessor, Phi-3.5-Mini, Phi-4-Mini features an expanded vocabulary size of 200K tokens to better support multilingual applications, as well as group query attention for more efficient long-sequence generation. Phi-4-Multimodal is a multimodal model that integrates text, vision, and speech/audio input modalities into a single model. Its novel modality extension approach leverages LoRA adapters and modality-specific routers to allow multiple inference modes combining various modalities without interference. For example, it now ranks first in the OpenASR leaderboard to date, although the LoRA component of the speech/audio modality has just 460 million parameters. Phi-4-Multimodal supports scenarios involving (vision + language), (vision + speech), and (speech/audio) inputs, outperforming larger vision-language and speech-language models on a wide range of tasks. Additionally, we experiment to further train Phi-4-Mini to enhance its reasoning capabilities. Despite its compact 3.8-billion-parameter size, this experimental version achieves reasoning performance on par with or surpassing significantly larger models, including DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B.

We introduce the Probabilistic Worldbuilding Model (PWM), a new fully-symbolic Bayesian model of semantic parsing and reasoning, as a first step in a research program toward more domain- and task-general NLU and AI. Humans create internal mental models of their observations which greatly aid in their ability to understand and reason about a large variety of problems. In PWM, the meanings of sentences, acquired facts about the world, and intermediate steps in reasoning are all expressed in a human-readable formal language, with the design goal of interpretability. PWM is Bayesian, designed specifically to be able to generalize to new domains and new tasks. We derive and implement an inference algorithm that reads sentences by parsing and abducing updates to its latent world model that capture the semantics of those sentences, and evaluate it on two out-of-domain question-answering datasets: (1) ProofWriter and (2) a new dataset we call FictionalGeoQA, designed to be more representative of real language but still simple enough to focus on evaluating reasoning ability, while being robust against heuristics. Our method outperforms baselines on both, thereby demonstrating its value as a proof-of-concept.

Transformers do not scale very well to long sequence lengths largely because of quadratic self-attention complexity. In the recent months, a wide spectrum of efficient, fast Transformers have been proposed to tackle this problem, more often than not claiming superior or comparable model quality to vanilla Transformer models. To this date, there is no well-established consensus on how to evaluate this class of models. Moreover, inconsistent benchmarking on a wide spectrum of tasks and datasets makes it difficult to assess relative model quality amongst many models. This paper proposes a systematic and unified benchmark, LRA, specifically focused on evaluating model quality under long-context scenarios. Our benchmark is a suite of tasks consisting of sequences ranging from 1K to 16K tokens, encompassing a wide range of data types and modalities such as text, natural, synthetic images, and mathematical expressions requiring similarity, structural, and visual-spatial reasoning. We systematically evaluate ten well-established long-range Transformer models (Reformers, Linformers, Linear Transformers, Sinkhorn Transformers, Performers, Synthesizers, Sparse Transformers, and Longformers) on our newly proposed benchmark suite. LRA paves the way towards better understanding this class of efficient Transformer models, facilitates more research in this direction, and presents new challenging tasks to tackle. Our benchmark code will be released at https://github.com/google-research/long-range-arena.

Recent works have shown that chain-of-thought (CoT) prompting can elicit language models to solve complex reasoning tasks, step-by-step. However, prompt-based CoT methods are dependent on very large models such as GPT-3 175B which are prohibitive to deploy at scale. In this paper, we use these large models as reasoning teachers to enable complex reasoning in smaller models and reduce model size requirements by several orders of magnitude. We propose Fine-tune-CoT, a method that generates reasoning samples from very large teacher models to fine-tune smaller models. We evaluate our method on a wide range of public models and complex tasks. We find that Fine-tune-CoT enables substantial reasoning capability in small models, far outperforming prompt-based baselines and even the teacher model in many tasks. Additionally, we extend our method by leveraging the teacher model's ability to generate multiple distinct rationales for each original sample. Enriching the fine-tuning data with such diverse reasoning results in a substantial performance boost across datasets, even for very small models. We conduct ablations and sample studies to understand the emergence of reasoning capabilities of student models. Our code implementation and data are available at https://github.com/itsnamgyu/reasoning-teacher.

This research delves into the construction and utilization of synthetic datasets, specifically within the telematics sphere, leveraging OpenAI's powerful language model, ChatGPT. Synthetic datasets present an effective solution to challenges pertaining to data privacy, scarcity, and control over variables - characteristics that make them particularly valuable for research pursuits. The utility of these datasets, however, largely depends on their quality, measured through the lenses of diversity, relevance, and coherence. To illustrate this data creation process, a hands-on case study is conducted, focusing on the generation of a synthetic telematics dataset. The experiment involved an iterative guidance of ChatGPT, progressively refining prompts and culminating in the creation of a comprehensive dataset for a hypothetical urban planning scenario in Columbus, Ohio. Upon generation, the synthetic dataset was subjected to an evaluation, focusing on the previously identified quality parameters and employing descriptive statistics and visualization techniques for a thorough analysis. Despite synthetic datasets not serving as perfect replacements for actual world data, their potential in specific use-cases, when executed with precision, is significant. This research underscores the potential of AI models like ChatGPT in enhancing data availability for complex sectors like telematics, thus paving the way for a myriad of new research opportunities.

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual reasoning. In contrast to previous studies that primarily focus on commonsense causal reasoning, where LLMs often rely on prior knowledge for inference, we specifically assess their ability to perform counterfactual inference using a set of formal rules. To support this evaluation, we introduce a new benchmark dataset, CounterBench, comprising 1K counterfactual reasoning questions. The dataset is designed with varying levels of difficulty, diverse causal graph structures, distinct types of counterfactual questions, and multiple nonsensical name variants. Our experiments demonstrate that counterfactual reasoning poses a significant challenge for LLMs, with most models performing at levels comparable to random guessing. To enhance LLM's counterfactual reasoning ability, we propose a novel reasoning paradigm, CoIn, which guides LLMs through iterative reasoning and backtracking to systematically explore counterfactual solutions. Experimental results show that our method significantly improves LLM performance on counterfactual reasoning tasks and consistently enhances performance across different LLMs.Our dataset is available at https://huggingface.co/datasets/CounterBench/CounterBench.

Recognizing if LLM output can be grounded in evidence is central to many tasks in NLP: retrieval-augmented generation, summarization, document-grounded dialogue, and more. Current approaches to this kind of "fact-checking" are based on verifying each piece of a model generation against potential evidence using an LLM. However, this process can be very computationally expensive, requiring many calls to LLMs to check a single response. In this work, we show how to build small models that have GPT-4-level performance but for 400x lower cost. We do this by constructing synthetic training data with GPT-4, which involves creating realistic yet challenging instances of factual errors via a structured generation procedure. Training on this data teaches models to check each fact in the claim and recognize synthesis of information across sentences. For evaluation, we unify pre-existing datasets into a benchmark LLM-AggreFact, collected from recent work on fact-checking and grounding LLM generations. Our best system MiniCheck-FT5 (770M parameters) outperforms all systems of comparable size and reaches GPT-4 accuracy. We release LLM-AggreFact, code for data synthesis, and models.

Open-source multimodal large language models (MLLMs) have shown significant potential in a broad range of multimodal tasks. However, their reasoning capabilities remain constrained by existing instruction-tuning datasets, which were predominately repurposed from academic datasets such as VQA, AI2D, and ChartQA. These datasets target simplistic tasks, and only provide phrase-level answers without any intermediate rationales. To address these challenges, we introduce a scalable and cost-effective method to construct a large-scale multimodal instruction-tuning dataset with rich intermediate rationales designed to elicit CoT reasoning. Using only open models, we create a dataset containing 12M instruction-response pairs to cover diverse, reasoning-intensive tasks with detailed and faithful rationales. Experiments demonstrate that training MLLMs on this dataset significantly improves reasoning capabilities, achieving state-of-the-art performance on benchmarks such as MathVerse (+8.1%), MMMU-Pro (+7%), and MuirBench (+13.3%). Additionally, the model demonstrates notable improvements of up to 4% on non-reasoning-based benchmarks. Ablation studies further highlight the importance of key components, such as rewriting and self-filtering, in the dataset construction process.

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary, limiting the generalizability of acquired reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. Then, using the proposed corpora, which we name FLD (Formal Logic Deduction), we first evaluate and analyze the logical reasoning ability of the latest LLMs. Even GPT-4 can solve only half of the problems, suggesting that pure logical reasoning isolated from knowledge is still challenging for the LLMs, and additional training specialized in logical reasoning is indeed essential. We next empirically verify that LMs trained on FLD corpora acquire more generalizable reasoning ability. Furthermore, we identify the aspects of reasoning ability on which deduction corpora can enhance LMs and those on which they cannot, and discuss future directions on each aspect. The released corpora serve both as learning resources and as challenging benchmarks.

Recent advancements in transformer-based models have initiated research interests in investigating their ability to learn to perform reasoning tasks. However, most of the contexts used for this purpose are in practice very simple: generated from short (fragments of) first-order logic sentences with only a few logical operators and quantifiers. In this work, we construct the natural language dataset, DELTA_D, using the description logic language ALCQ. DELTA_D contains 384K examples, and increases in two dimensions: i) reasoning depth, and ii) linguistic complexity. In this way, we systematically investigate the reasoning ability of a supervised fine-tuned DeBERTa-based model and of two large language models (GPT-3.5, GPT-4) with few-shot prompting. Our results demonstrate that the DeBERTa-based model can master the reasoning task and that the performance of GPTs can improve significantly even when a small number of samples is provided (9 shots). We open-source our code and datasets.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Logical reasoning is a critical component of Large Language Models (LLMs), and substantial research efforts in recent years have aimed to enhance their deductive reasoning capabilities. However, existing deductive reasoning benchmarks, which are crucial for evaluating and advancing LLMs, are inadequate due to their lack of task complexity, presence of prior knowledge as a confounder, and superficial error analysis. To address these deficiencies, we introduce JustLogic, a synthetically generated deductive reasoning benchmark designed for rigorous evaluation of LLMs. JustLogic is (i) highly complex, capable of generating a diverse range of linguistic patterns, vocabulary, and argument structures; (ii) prior knowledge independent, eliminating the advantage of models possessing prior knowledge and ensuring that only deductive reasoning is used to answer questions; and (iii) capable of in-depth error analysis on the heterogeneous effects of reasoning depth and argument form on model accuracy. Our experimental results on JustLogic reveal that most state-of-the-art (SOTA) LLMs perform significantly worse than the human average, demonstrating substantial room for model improvement. All code and data are available at https://github.com/michaelchen-lab/JustLogic

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

The availability of high-quality data is one of the most important factors in improving the reasoning capability of LLMs. Existing works have demonstrated the effectiveness of creating more instruction data from seed questions or knowledge bases. Recent research indicates that continually scaling up data synthesis from strong models (e.g., GPT-4) can further elicit reasoning performance. Though promising, the open-sourced community still lacks high-quality data at scale and scalable data synthesis methods with affordable costs. To address this, we introduce ScaleQuest, a scalable and novel data synthesis method that utilizes "small-size" (e.g., 7B) open-source models to generate questions from scratch without the need for seed data with complex augmentation constraints. With the efficient ScaleQuest, we automatically constructed a mathematical reasoning dataset consisting of 1 million problem-solution pairs, which are more effective than existing open-sourced datasets. It can universally increase the performance of mainstream open-source models (i.e., Mistral, Llama3, DeepSeekMath, and Qwen2-Math) by achieving 29.2% to 46.4% gains on MATH. Notably, simply fine-tuning the Qwen2-Math-7B-Base model with our dataset can even surpass Qwen2-Math-7B-Instruct, a strong and well-aligned model on closed-source data, and proprietary models such as GPT-4-Turbo and Claude-3.5 Sonnet.

Large Language Models (LLMs) have demonstrated impressive real-world utility, exemplifying artificial useful intelligence (AUI). However, their ability to reason adaptively and robustly -- the hallmarks of artificial general intelligence (AGI) -- remains fragile. While LLMs seemingly succeed in commonsense reasoning, programming, and mathematics, they struggle to generalize algorithmic understanding across novel contexts. Our experiments with algorithmic tasks in esoteric programming languages reveal that LLM's reasoning overfits to the training data and is limited in its transferability. We hypothesize that the core issue underlying such limited transferability is the coupling of reasoning and knowledge in LLMs. To transition from AUI to AGI, we propose disentangling knowledge and reasoning through three key directions: (1) pretaining to reason using RL from scratch as an alternative to the widely used next-token prediction pretraining, (2) using a curriculum of synthetic tasks to ease the learning of a reasoning prior for RL that can then be transferred to natural language tasks, and (3) learning more generalizable reasoning functions using a small context window to reduce exploiting spurious correlations between tokens. Such a reasoning system coupled with a trained retrieval system and a large external memory bank as a knowledge store can overcome several limitations of existing architectures at learning to reason in novel scenarios.

Understanding the mathematical reasoning capabilities of Large Language Models (LLMs) is a central topic in the study of artificial intelligence. This new domain necessitates the creation of datasets of reasoning tasks for both training and benchmarking the performance of LLMs. To this end, we introduce the Karp dataset: The first dataset composed of detailed proofs of NP-completeness reductions. The reductions vary in difficulty, ranging from simple exercises of undergraduate courses to more challenging reductions from academic papers. We compare the performance of state-of-the-art models on this task and demonstrate the effect of fine-tuning with the Karp dataset on reasoning capacity.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study investigating the detection of formally valid inferences in controlled fragments of natural language for which the satisfiability problem becomes increasingly complex. We find that, while transformer-based language models perform surprisingly well in these scenarios, a deeper analysis re-veals that they appear to overfit to superficial patterns in the data rather than acquiring the logical principles governing the reasoning in these fragments.

Post-training Large Language Models (LLMs) with explicit reasoning trajectories can enhance their reasoning abilities. However, acquiring such high-quality trajectory data typically demands meticulous supervision from humans or superior models, which can be either expensive or license-constrained. In this paper, we explore how far an LLM can improve its reasoning by self-synthesizing reasoning paths as training data without any additional supervision. Existing self-synthesizing methods, such as STaR, suffer from poor generalization to out-of-domain (OOD) reasoning tasks. We hypothesize it is due to that their self-synthesized reasoning paths are too task-specific, lacking general task-agnostic reasoning guidance. To address this, we propose Reasoning Generalist via Self-Improvement (ReGenesis), a method to self-synthesize reasoning paths as post-training data by progressing from abstract to concrete. More specifically, ReGenesis self-synthesizes reasoning paths by converting general reasoning guidelines into task-specific ones, generating reasoning structures, and subsequently transforming these structures into reasoning paths, without the need for human-designed task-specific examples used in existing methods. We show that ReGenesis achieves superior performance on all in-domain and OOD settings tested compared to existing methods. For six OOD tasks specifically, while previous methods exhibited an average performance decrease of approximately 4.6% after post training, ReGenesis delivers around 6.1% performance improvement. We also conduct in-depth analysis of our framework and show ReGenesis is effective across various LLMs and design choices.

Large language models (LLMs) have demonstrated impressive reasoning capabilities, yet there is ongoing debate about these abilities and the potential data contamination problem recently. This paper aims to evaluate the reasoning capacities of LLMs, specifically in solving recent competition-level programming problems in Codeforces, which are expert-crafted and unique, requiring deep understanding and robust reasoning skills. We first provide a comprehensive evaluation of GPT-4's peiceived zero-shot performance on this task, considering various aspects such as problems' release time, difficulties, and types of errors encountered. Surprisingly, the peiceived performance of GPT-4 has experienced a cliff like decline in problems after September 2021 consistently across all the difficulties and types of problems, which shows the potential data contamination, as well as the challenges for any existing LLM to solve unseen complex reasoning problems. We further explore various approaches such as fine-tuning, Chain-of-Thought prompting and problem description simplification, unfortunately none of them is able to consistently mitigate the challenges. Through our work, we emphasis the importance of this excellent data source for assessing the genuine reasoning capabilities of LLMs, and foster the development of LLMs with stronger reasoning abilities and better generalization in the future.

Eliciting reasoning capabilities from language models (LMs) is a critical direction on the path towards building intelligent systems. Most recent studies dedicated to reasoning focus on out-of-distribution performance on procedurally-generated synthetic benchmarks, bespoke-built to evaluate specific skills only. This trend makes results hard to transfer across publications, slowing down progress. Three years ago, a similar issue was identified and rectified in the field of neural algorithmic reasoning, with the advent of the CLRS benchmark. CLRS is a dataset generator comprising graph execution traces of classical algorithms from the Introduction to Algorithms textbook. Inspired by this, we propose CLRS-Text -- a textual version of these algorithmic traces. Out of the box, CLRS-Text is capable of procedurally generating trace data for thirty diverse, challenging algorithmic tasks across any desirable input distribution, while offering a standard pipeline in which any additional algorithmic tasks may be created in the benchmark. We fine-tune and evaluate various LMs as generalist executors on this benchmark, validating prior work and revealing a novel, interesting challenge for the LM reasoning community. Our code is available at https://github.com/google-deepmind/clrs/tree/master/clrs/_src/clrs_text.

Artificial Intelligence (AI) advancement is heavily dependent on access to large-scale, high-quality training data. However, in specialized domains such as healthcare, data acquisition faces significant constraints due to privacy regulations, ethical considerations, and limited availability. While synthetic data generation offers a promising solution, conventional approaches typically require substantial real data for training generative models. The emergence of large-scale prompt-based models presents new opportunities for synthetic data generation without direct access to protected data. However, crafting effective prompts for domain-specific data generation remains challenging, and manual prompt engineering proves insufficient for achieving output with sufficient precision and authenticity. We review recent developments in automatic prompt optimization, following PRISMA guidelines. We analyze six peer-reviewed studies published between 2020 and 2024 that focus on automatic data-free prompt optimization methods. Our analysis reveals three approaches: feedback-driven, error-based, and control-theoretic. Although all approaches demonstrate promising capabilities in prompt refinement and adaptation, our findings suggest the need for an integrated framework that combines complementary optimization techniques to enhance synthetic data generation while minimizing manual intervention. We propose future research directions toward developing robust, iterative prompt optimization frameworks capable of improving the quality of synthetic data. This advancement can be particularly crucial for sensitive fields and in specialized domains where data access is restricted, potentially transforming how we approach synthetic data generation for AI development.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

Large Language Models exhibit impressive reasoning capabilities across diverse tasks, motivating efforts to distill these capabilities into smaller models through generated reasoning data. However, direct training on such synthesized reasoning data may lead to superficial imitation of reasoning process, rather than fostering a genuine integration of reasoning capabilities with underlying knowledge. To address this, we propose TinyThinker, a framework introducing two novel approaches. First, we introduce a three-stage process that incrementally guides the student model through the reasoning process, progressively refining knowledge from coarse to fine granularity. Second, we develop a two-phase training framework comprising an initial reasoning acquisition phase followed by a self-reflection phase utilizing self-generated data. Experiments on commonsense reasoning benchmarks demonstrate that TinyThinker achieves superior performance compared to baselines. Ablation studies further validate the effectiveness of each component in our framework. TinyThinker is extendable to other knowledge-intensive reasoning tasks, offering an alternative strategy for developing effective reasoning capabilities in smaller language models. Codes are available at https://github.com/shengminp/TinyThinker

Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However, formal language can cause systematic problems for inductive reasoning such as disability of handling raw input such as natural language, sensitiveness to mislabeled data, and incapacity to handle ambiguous input. To this end, we propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts, and create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. New automatic metrics are also proposed and analysed for the evaluation of this task. With DEER, we investigate a modern approach for inductive reasoning where we use natural language as representation for knowledge instead of formal language and use pretrained language models as ''reasoners''. Moreover, we provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts. We also propose a new framework drawing insights from philosophy literature for this task, which we show in the experiment section that surpasses baselines in both automatic and human evaluations. We discuss about our future perspectives for inductive reasoning in Section 7. Dataset and code are available at https://github.com/ZonglinY/Inductive_Reasoning.

Harnessing logical reasoning ability is a comprehensive natural language understanding endeavor. With the release of Generative Pretrained Transformer 4 (GPT-4), highlighted as "advanced" at reasoning tasks, we are eager to learn the GPT-4 performance on various logical reasoning tasks. This report analyses multiple logical reasoning datasets, with popular benchmarks like LogiQA and ReClor, and newly-released datasets like AR-LSAT. We test the multi-choice reading comprehension and natural language inference tasks with benchmarks requiring logical reasoning. We further construct a logical reasoning out-of-distribution dataset to investigate the robustness of ChatGPT and GPT-4. We also make a performance comparison between ChatGPT and GPT-4. Experiment results show that ChatGPT performs significantly better than the RoBERTa fine-tuning method on most logical reasoning benchmarks. With early access to the GPT-4 API we are able to conduct intense experiments on the GPT-4 model. The results show GPT-4 yields even higher performance on most logical reasoning datasets. Among benchmarks, ChatGPT and GPT-4 do relatively well on well-known datasets like LogiQA and ReClor. However, the performance drops significantly when handling newly released and out-of-distribution datasets. Logical reasoning remains challenging for ChatGPT and GPT-4, especially on out-of-distribution and natural language inference datasets. We release the prompt-style logical reasoning datasets as a benchmark suite and name it LogiEval.

The capabilities and limitations of Large Language Models have been sketched out in great detail in recent years, providing an intriguing yet conflicting picture. On the one hand, LLMs demonstrate a general ability to solve problems. On the other hand, they show surprising reasoning gaps when compared to humans, casting doubt on the robustness of their generalisation strategies. The sheer volume of data used in the design of LLMs has precluded us from applying the method traditionally used to measure generalisation: train-test set separation. To overcome this, we study what kind of generalisation strategies LLMs employ when performing reasoning tasks by investigating the pretraining data they rely on. For two models of different sizes (7B and 35B) and 2.5B of their pretraining tokens, we identify what documents influence the model outputs for three simple mathematical reasoning tasks and contrast this to the data that are influential for answering factual questions. We find that, while the models rely on mostly distinct sets of data for each factual question, a document often has a similar influence across different reasoning questions within the same task, indicating the presence of procedural knowledge. We further find that the answers to factual questions often show up in the most influential data. However, for reasoning questions the answers usually do not show up as highly influential, nor do the answers to the intermediate reasoning steps. When we characterise the top ranked documents for the reasoning questions qualitatively, we confirm that the influential documents often contain procedural knowledge, like demonstrating how to obtain a solution using formulae or code. Our findings indicate that the approach to reasoning the models use is unlike retrieval, and more like a generalisable strategy that synthesises procedural knowledge from documents doing a similar form of reasoning.

With the recent advance in large pre-trained language models, researchers have achieved record performances in NLP tasks that mostly focus on language pattern matching. The community is experiencing the shift of the challenge from how to model language to the imitation of complex reasoning abilities like human beings. In this work, we investigate the application domain of finance that involves real-world, complex numerical reasoning. We propose a new large-scale dataset, ConvFinQA, aiming to study the chain of numerical reasoning in conversational question answering. Our dataset poses great challenge in modeling long-range, complex numerical reasoning paths in real-world conversations. We conduct comprehensive experiments and analyses with both the neural symbolic methods and the prompting-based methods, to provide insights into the reasoning mechanisms of these two divisions. We believe our new dataset should serve as a valuable resource to push forward the exploration of real-world, complex reasoning tasks as the next research focus. Our dataset and code is publicly available at https://github.com/czyssrs/ConvFinQA.

Large language models demonstrate exceptional performance in simple code generation tasks but still face challenges in tackling complex problems. These challenges may stem from insufficient reasoning and problem decomposition capabilities. To address this issue, we propose a reasoning-augmented data generation process, SRA-MCTS, which guides the model to autonomously generate high-quality intermediate reasoning paths. This creates a positive feedback loop, enabling continuous improvement. Our method operates entirely through the model itself without requiring additional supervision. By synthesizing natural language reasoning paths and translating them into executable code, the approach ensures analytical accuracy and enhances the success rate in solving complex tasks. Experimental results show that, even without additional supervisory signals, our method achieves performance improvements across different model scales, demonstrating the significant potential of self-improvement in small models. Furthermore, the method remains robust when traditional Chain-of-Thought (CoT) approaches exhibit performance degradation, with notable improvements observed in diversity metrics such as pass@10. We encourage further exploration of reasoning processes within training data to enhance the ability of language models to address complex problems. Our code and data are public at https://github.com/DIRECT-BIT/SRA-MCTS.

Current inference scaling methods, such as Self-consistency and Best-of-N, have proven effective in improving the accuracy of LLMs on complex reasoning tasks. However, these methods rely heavily on the quality of candidate responses and are unable to produce correct answers when all candidates are incorrect. In this paper, we propose a novel inference scaling strategy, CoT-based Synthesizer, which leverages CoT reasoning to synthesize superior answers by analyzing complementary information from multiple candidate responses, even when all candidate responses are flawed. To enable a lightweight and cost-effective implementation, we introduce an automated data generation pipeline that creates diverse training data. This allows smaller LLMs trained on this data to improve the inference accuracy of larger models, including API-based LLMs. Experimental results across four benchmark datasets with seven policy models demonstrate that our method significantly enhances performance, with gains of 11.8% for Llama3-8B and 10.3% for GPT-4o on the MATH dataset. The corresponding training data and code are publicly available on https://github.com/RUCKBReasoning/CoT-based-Synthesizer.

Despite rapid advancements in large language models (LLMs), QG remains a challenging problem due to its complicated process, open-ended nature, and the diverse settings in which question generation occurs. A common approach to address these challenges involves fine-tuning smaller, custom models using datasets containing background context, question, and answer. However, obtaining suitable domain-specific datasets with appropriate context is often more difficult than acquiring question-answer pairs. In this paper, we investigate training QG models using synthetic contexts generated by LLMs from readily available question-answer pairs. We conduct a comprehensive study to answer critical research questions related to the performance of models trained on synthetic contexts and their potential impact on QG research and applications. Our empirical results reveal: 1) contexts are essential for QG tasks, even if they are synthetic; 2) fine-tuning smaller language models has the capability of achieving better performances as compared to prompting larger language models; and 3) synthetic context and real context could achieve comparable performances. These findings highlight the effectiveness of synthetic contexts in QG and paves the way for future advancements in the field.

The reasoning steps generated by LLMs might be incomplete, as they mimic logical leaps common in everyday communication found in their pre-training data: underlying rationales are frequently left implicit (unstated). To address this challenge, we introduce RATIONALYST, a model for process-supervision of reasoning based on pre-training on a vast collection of rationale annotations extracted from unlabeled data. We extract 79k rationales from web-scale unlabelled dataset (the Pile) and a combination of reasoning datasets with minimal human intervention. This web-scale pre-training for reasoning allows RATIONALYST to consistently generalize across diverse reasoning tasks, including mathematical, commonsense, scientific, and logical reasoning. Fine-tuned from LLaMa-3-8B, RATIONALYST improves the accuracy of reasoning by an average of 3.9% on 7 representative reasoning benchmarks. It also demonstrates superior performance compared to significantly larger verifiers like GPT-4 and similarly sized models fine-tuned on matching training sets.

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam et al. (2024); Zecevic et al. (2023); Wu et al. (2024) highlight a significant gap between their language proficiency and reasoning abilities. Reasoning in LLMs and Vision Language Models (VLMs) aims to bridge this gap by enabling these models to think and re-evaluate their actions and responses. Reasoning is an essential capability for complex problem-solving and a necessary step toward establishing trust in Artificial Intelligence (AI). This will make AI suitable for deployment in sensitive domains, such as healthcare, banking, law, defense, security etc. In recent times, with the advent of powerful reasoning models like OpenAI O1 and DeepSeek R1, reasoning endowment has become a critical research topic in LLMs. In this paper, we provide a detailed overview and comparison of existing reasoning techniques and present a systematic survey of reasoning-imbued language models. We also study current challenges and present our findings.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Recently, large-scale pre-trained language models have demonstrated impressive performance on several commonsense-reasoning benchmark datasets. However, building machines with commonsense to compose realistically plausible sentences remains challenging. In this paper, we present a constrained text generation task, CommonGen associated with a benchmark dataset, to explicitly test machines for the ability of generative commonsense reasoning. Given a set of common concepts (e.g., {dog, frisbee, catch, throw}); the task is to generate a coherent sentence describing an everyday scenario using these concepts (e.g., "a man throws a frisbee and his dog catches it"). The CommonGen task is challenging because it inherently requires 1) relational reasoning with background commonsense knowledge, and 2) compositional generalization ability to work on unseen concept combinations. Our dataset, constructed through a combination of crowdsourced and existing caption corpora, consists of 79k commonsense descriptions over 35k unique concept-sets. Experiments show that there is a large gap between state-of-the-art text generation models (e.g., T5) and human performance. Furthermore, we demonstrate that the learned generative commonsense reasoning capability can be transferred to improve downstream tasks such as CommonsenseQA by generating additional context.

Given questions regarding some prototypical situation such as Name something that people usually do before they leave the house for work? a human can easily answer them via acquired experiences. There can be multiple right answers for such questions, with some more common for a situation than others. This paper introduces a new question answering dataset for training and evaluating common sense reasoning capabilities of artificial intelligence systems in such prototypical situations. The training set is gathered from an existing set of questions played in a long-running international game show FAMILY- FEUD. The hidden evaluation set is created by gathering answers for each question from 100 crowd-workers. We also propose a generative evaluation task where a model has to output a ranked list of answers, ideally covering all prototypical answers for a question. After presenting multiple competitive baseline models, we find that human performance still exceeds model scores on all evaluation metrics with a meaningful gap, supporting the challenging nature of the task.

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Language models can store vast amounts of factual knowledge, but their ability to use this knowledge for logical reasoning remains questionable. This paper explores a language model's ability to manipulate its stored knowledge during inference. We focus on four manipulation types: retrieval (e.g., "What is person A's attribute X"), classification (e.g., "Is A's attribute X even or odd?"), comparison (e.g., "Is A greater than B in attribute X?") and inverse search (e.g., "Which person's attribute X equals T?") We observe that pre-trained language models like GPT2/3/4 excel in knowledge retrieval but struggle with simple classification or comparison tasks unless Chain of Thoughts (CoTs) are employed during both training and inference. They also perform poorly in inverse knowledge search, irrespective of the prompts. Our primary contribution is a synthetic dataset for a controlled experiment that confirms these inherent weaknesses: a language model cannot efficiently manipulate knowledge from pre-training data, even when such knowledge is perfectly stored and fully extractable in the models, and despite adequate instruct fine-tuning.

Recently, large language models (LLMs), including notable models such as GPT-4 and burgeoning community models, have showcased significant general language understanding abilities. However, there has been a scarcity of attempts to assess the logical reasoning capacities of these LLMs, an essential facet of natural language understanding. To encourage further investigation in this area, we introduce GLoRE, a meticulously assembled General Logical Reasoning Evaluation benchmark comprised of 12 datasets that span three different types of tasks. Our experimental results show that compared to the performance of human and supervised fine-tuning, the logical reasoning capabilities of open LLM models necessitate additional improvement; ChatGPT and GPT-4 show a strong capability of logical reasoning, with GPT-4 surpassing ChatGPT by a large margin. We propose a self-consistency probing method to enhance the accuracy of ChatGPT and a fine-tuned method to boost the performance of an open LLM. We release the datasets and evaluation programs to facilitate future research.

Large language models (LLMs) have exhibited complex reasoning abilities by generating question rationales and demonstrated exceptional performance in natural language processing (NLP) tasks. However, these reasoning capabilities generally emerge in models with tens of billions of parameters, creating significant computational challenges for real-world deployment. Recent research has concentrated on improving open-source smaller models through knowledge distillation (KD) from commercial LLMs. Nevertheless, most of these studies rely solely on the responses from one single LLM as the gold rationale for training. In this paper, we introduce a novel Mistake-Aware Peer-Review Distillation (MAPD) approach: 1) Instead of merely obtaining gold rationales from teachers, our method asks teachers to identify and explain the student's mistakes, providing customized instruction learning data. 2) We design a simulated peer-review process between teacher LLMs, which selects only the generated rationales above the acceptance threshold. This reduces the chance of teachers guessing correctly with flawed rationale, improving instructional data quality. Comprehensive experiments and analysis on mathematical, commonsense, and logical reasoning tasks demonstrate the effectiveness of our method.

Large language models have been shown to suffer from reasoning inconsistency issues. That is, they fail more in situations unfamiliar to the training data, even though exact or very similar reasoning paths exist in more common cases that they can successfully solve. Such observations motivate us to propose methods that encourage models to understand the high-level and abstract reasoning processes during training instead of only the final answer. This way, models can transfer the exact solution to similar cases, regardless of their relevance to the pre-training data distribution. In this work, we propose SAL, a self-supervised analogical learning framework. SAL mimics the human analogy process and trains models to explicitly transfer high-quality symbolic solutions from cases that they know how to solve to other rare cases in which they tend to fail more. We show that the resulting models after SAL learning outperform base language models on a wide range of reasoning benchmarks, such as StrategyQA, GSM8K, and HotpotQA, by 2% to 20%. At the same time, we show that our model is more generalizable and controllable through analytical studies.

Training giant models from scratch for each complex task is resource- and data-inefficient. To help develop models that can leverage existing systems, we propose a new challenge: Learning to solve complex tasks by communicating with existing agents (or models) in natural language. We design a synthetic benchmark, CommaQA, with three complex reasoning tasks (explicit, implicit, numeric) designed to be solved by communicating with existing QA agents. For instance, using text and table QA agents to answer questions such as "Who had the longest javelin throw from USA?". We show that black-box models struggle to learn this task from scratch (accuracy under 50\%) even with access to each agent's knowledge and gold facts supervision. In contrast, models that learn to communicate with agents outperform black-box models, reaching scores of 100\% when given gold decomposition supervision. However, we show that the challenge of learning to solve complex tasks by communicating with existing agents without relying on any auxiliary supervision or data still remains highly elusive. We release CommaQA, along with a compositional generalization test split, to advance research in this direction. Dataset and Code available at https://github.com/allenai/commaqa.

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for behavioral studies. However, these studies do not provide insights into the internal mechanisms driving the observed capabilities. To improve our understanding of the internal mechanisms of transformers, we present a comprehensive mechanistic analysis of a transformer trained on a synthetic reasoning task. We identify a set of interpretable mechanisms the model uses to solve the task, and validate our findings using correlational and causal evidence. Our results suggest that it implements a depth-bounded recurrent mechanisms that operates in parallel and stores intermediate results in selected token positions. We anticipate that the motifs we identified in our synthetic setting can provide valuable insights into the broader operating principles of transformers and thus provide a basis for understanding more complex models.

Large pre-trained language models (LMs) are known to encode substantial amounts of linguistic information. However, high-level reasoning skills, such as numerical reasoning, are difficult to learn from a language-modeling objective only. Consequently, existing models for numerical reasoning have used specialized architectures with limited flexibility. In this work, we show that numerical reasoning is amenable to automatic data generation, and thus one can inject this skill into pre-trained LMs, by generating large amounts of data, and training in a multi-task setup. We show that pre-training our model, GenBERT, on this data, dramatically improves performance on DROP (49.3 rightarrow 72.3 F1), reaching performance that matches state-of-the-art models of comparable size, while using a simple and general-purpose encoder-decoder architecture. Moreover, GenBERT generalizes well to math word problem datasets, while maintaining high performance on standard RC tasks. Our approach provides a general recipe for injecting skills into large pre-trained LMs, whenever the skill is amenable to automatic data augmentation.

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Recent advancements have significantly augmented the reasoning capabilities of Large Language Models (LLMs) through various methodologies, especially chain-of-thought (CoT) reasoning. However, previous methods fail to address reasoning errors in intermediate steps, leading to accumulative errors. In this paper, we propose Deductive Beam Search (DBS), which seamlessly integrates CoT and deductive reasoning with step-wise beam search for LLMs. Our approach deploys a verifier, verifying the deducibility of a reasoning step and its premises, thus alleviating the error accumulation. Furthermore, we introduce a scalable and labor-free data construction method to amplify our model's verification capabilities. Extensive experiments demonstrate that our approach significantly enhances the base performance of LLMs of various scales (7B, 13B, 70B, and ChatGPT) across 8 reasoning datasets from 3 diverse reasoning genres, including arithmetic, commonsense, and symbolic. Moreover, our analysis proves DBS's capability of detecting diverse and subtle reasoning errors and robustness on different model scales.

Multi-modal Large Language Models (MLLMs) are increasingly prominent in the field of artificial intelligence. These models not only excel in traditional vision-language tasks but also demonstrate impressive performance in contemporary multi-modal benchmarks. Although many of these benchmarks attempt to holistically evaluate MLLMs, they typically concentrate on basic reasoning tasks, often yielding only simple yes/no or multi-choice responses. These methods naturally lead to confusion and difficulties in conclusively determining the reasoning capabilities of MLLMs. To mitigate this issue, we manually curate a benchmark dataset specifically designed for MLLMs, with a focus on complex reasoning tasks. Our benchmark comprises three key reasoning categories: deductive, abductive, and analogical reasoning. The queries in our dataset are intentionally constructed to engage the reasoning capabilities of MLLMs in the process of generating answers. For a fair comparison across various MLLMs, we incorporate intermediate reasoning steps into our evaluation criteria. In instances where an MLLM is unable to produce a definitive answer, its reasoning ability is evaluated by requesting intermediate reasoning steps. If these steps align with our manual annotations, appropriate scores are assigned. This evaluation scheme resembles methods commonly used in human assessments, such as exams or assignments, and represents what we consider a more effective assessment technique compared with existing benchmarks. We evaluate a selection of representative MLLMs using this rigorously developed open-ended multi-step elaborate reasoning benchmark, designed to challenge and accurately measure their reasoning capabilities. The code and data will be released at https://core-mm.github.io/

Generative Pre-trained Transformer 4 (GPT-4) demonstrates impressive chain-of-thought reasoning ability. Recent work on self-instruction tuning, such as Alpaca, has focused on enhancing the general proficiency of models. These instructions enable the model to achieve performance comparable to GPT-3.5 on general tasks like open-domain text generation and paraphrasing. However, they fall short of helping the model handle complex reasoning tasks. To bridge the gap, this paper presents LogiCoT, a new instruction-tuning dataset for Logical Chain-of-Thought reasoning with GPT-4. We elaborate on the process of harvesting instructions for prompting GPT-4 to generate chain-of-thought rationales. LogiCoT serves as an instruction set for teaching models of logical reasoning and elicits general reasoning skills.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Logical reasoning is of vital importance to natural language understanding. Previous studies either employ graph-based models to incorporate prior knowledge about logical relations, or introduce symbolic logic into neural models through data augmentation. These methods, however, heavily depend on annotated training data, and thus suffer from over-fitting and poor generalization problems due to the dataset sparsity. To address these two problems, in this paper, we propose MERIt, a MEta-path guided contrastive learning method for logical ReasonIng of text, to perform self-supervised pre-training on abundant unlabeled text data. Two novel strategies serve as indispensable components of our method. In particular, a strategy based on meta-path is devised to discover the logical structure in natural texts, followed by a counterfactual data augmentation strategy to eliminate the information shortcut induced by pre-training. The experimental results on two challenging logical reasoning benchmarks, i.e., ReClor and LogiQA, demonstrate that our method outperforms the SOTA baselines with significant improvements.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Recent advances in large language models (LLMs) have demonstrated notable progress on many mathematical benchmarks. However, most of these benchmarks only feature problems grounded in junior and senior high school subjects, contain only multiple-choice questions, and are confined to a limited scope of elementary arithmetic operations. To address these issues, this paper introduces an expansive benchmark suite SciBench that aims to systematically examine the reasoning capabilities required for complex scientific problem solving. SciBench contains two carefully curated datasets: an open set featuring a range of collegiate-level scientific problems drawn from mathematics, chemistry, and physics textbooks, and a closed set comprising problems from undergraduate-level exams in computer science and mathematics. Based on the two datasets, we conduct an in-depth benchmark study of two representative LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with an overall score of merely 35.80%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms others and some strategies that demonstrate improvements in certain problem-solving skills result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

In this paper, we present and implement a multi-dimensional, modular framework for performing deep argument analysis (DeepA2) using current pre-trained language models (PTLMs). ArgumentAnalyst -- a T5 model (Raffel et al. 2020) set up and trained within DeepA2 -- reconstructs argumentative texts, which advance an informal argumentation, as valid arguments: It inserts, e.g., missing premises and conclusions, formalizes inferences, and coherently links the logical reconstruction to the source text. We create a synthetic corpus for deep argument analysis, and evaluate ArgumentAnalyst on this new dataset as well as on existing data, specifically EntailmentBank (Dalvi et al. 2021). Our empirical findings vindicate the overall framework and highlight the advantages of a modular design, in particular its ability to emulate established heuristics (such as hermeneutic cycles), to explore the model's uncertainty, to cope with the plurality of correct solutions (underdetermination), and to exploit higher-order evidence.

We explore whether Large Language Models (LLMs) are capable of logical reasoning with distorted facts, which we call Deduction under Perturbed Evidence (DUPE). DUPE presents a unique challenge to LLMs since they typically rely on their parameters, which encode mostly accurate information, to reason and make inferences. However, in DUPE, LLMs must reason over manipulated or falsified evidence present in their prompts, which can result in false conclusions that are valid only under the manipulated evidence. Our goal with DUPE is to determine whether LLMs can arrive at these false conclusions and identify whether the dominant factor influencing the deduction process is the encoded data in the parameters or the manipulated evidence in the prompts. To evaluate the DUPE capabilities of LLMs, we create a DUPEd version of the StrategyQA dataset, where facts are manipulated to reverse the answer to the question. Our findings show that even the most advanced GPT models struggle to reason on manipulated facts - showcasing poor DUPE skills - with accuracy dropping by 45% compared to the original dataset. We also investigate prompt settings inspired from student simulation models, which mitigate the accuracy drop to some extent. Our findings have practical implications for understanding the performance of LLMs in real-world applications such as student simulation models that involve reasoning over inaccurate information.

Most existing multi-hop datasets are extractive answer datasets, where the answers to the questions can be extracted directly from the provided context. This often leads models to use heuristics or shortcuts instead of performing true multi-hop reasoning. In this paper, we propose a new multi-hop dataset, MoreHopQA, which shifts from extractive to generative answers. Our dataset is created by utilizing three existing multi-hop datasets: HotpotQA, 2WikiMultihopQA, and MuSiQue. Instead of relying solely on factual reasoning, we enhance the existing multi-hop questions by adding another layer of questioning that involves one, two, or all three of the following types of reasoning: commonsense, arithmetic, and symbolic. Our dataset is created through a semi-automated process, resulting in a dataset with 1,118 samples that have undergone human verification. We then use our dataset to evaluate five different large language models: Mistral 7B, Gemma 7B, Llama 3 (8B and 70B), and GPT-4. We also design various cases to analyze the reasoning steps in the question-answering process. Our results show that models perform well on initial multi-hop questions but struggle with our extended questions, indicating that our dataset is more challenging than previous ones. Our analysis of question decomposition reveals that although models can correctly answer questions, only a portion - 38.7% for GPT-4 and 33.4% for Llama3-70B - achieve perfect reasoning, where all corresponding sub-questions are answered correctly. Evaluation code and data are available at https://github.com/Alab-NII/morehopqa

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

Reasoning is most powerful when an LLM accurately aggregates relevant information. We examine the critical role of information aggregation in reasoning by requiring the LLM to analyze sports narratives. To succeed at this task, an LLM must infer points from actions, identify related entities, attribute points accurately to players and teams, and compile key statistics to draw conclusions. We conduct comprehensive experiments with real NBA basketball data and present SportsGen, a new method to synthesize game narratives. By synthesizing data, we can rigorously evaluate LLMs' reasoning capabilities under complex scenarios with varying narrative lengths and density of information. Our findings show that most models, including GPT-4o, often fail to accurately aggregate basketball scores due to frequent scoring patterns. Open-source models like Llama-3 further suffer from significant score hallucinations. Finally, the effectiveness of reasoning is influenced by narrative complexity, information density, and domain-specific terms, highlighting the challenges in analytical reasoning tasks.

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two improved methods with significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Logical reasoning task has attracted great interest since it was proposed. Faced with such a task, current competitive models, even large language models (e.g., ChatGPT and PaLM 2), still perform badly. Previous promising LMs struggle in logical consistency modeling and logical structure perception. To this end, we model the logical reasoning task by transforming each logical sample into reasoning paths and propose an architecture PathReasoner. It addresses the task from the views of both data and model. To expand the diversity of the logical samples, we propose an atom extension strategy supported by equivalent logical formulas, to form new reasoning paths. From the model perspective, we design a stack of transformer-style blocks. In particular, we propose a path-attention module to joint model in-atom and cross-atom relations with the high-order diffusion strategy. Experiments show that PathReasoner achieves competitive performances on two logical reasoning benchmarks and great generalization abilities.

Prompt engineering is a challenging yet crucial task for optimizing the performance of large language models (LLMs). It requires complex reasoning to examine the model's errors, hypothesize what is missing or misleading in the current prompt, and communicate the task with clarity. While recent works indicate that LLMs can be meta-prompted to perform automatic prompt engineering, their potentials may not be fully untapped due to the lack of sufficient guidance to elicit complex reasoning capabilities in LLMs in the meta-prompt. In this work, we investigate the problem of "prompt engineering a prompt engineer" -- constructing a meta-prompt that more effectively guides LLMs to perform automatic prompt engineering. We introduce and analyze key components, such as a step-by-step reasoning template and context specification, which lead to improved performance. In addition, inspired by common optimization concepts such as batch size, step size and momentum, we introduce their verbalized counterparts to the meta-prompt and investigate their effects. Our final method, named PE2, finds a prompt that outperforms "let's think step by step" by 6.3% on the MultiArith dataset and 3.1% on the GSM8K dataset. To demonstrate its versatility, we apply PE2 to the Instruction Induction benchmark, a suite of counterfactual tasks, and a lengthy, real-world industrial prompt. In these settings, PE2 achieves strong performance and outperforms prior automatic prompt engineering baselines. Further, we show that PE2 makes meaningful and targeted prompt edits, amends erroneous or incomplete prompts, and presents non-trivial counterfactual reasoning abilities.

Despite their linguistic competence, Large Language models (LLMs) often exhibit limitations in their ability to reason reliably and flexibly. To address this, we propose a neurosymbolic approach that prompts LLMs to extract and encode all relevant information from a problem statement as logical code statements, and then use a logic programming language (Prolog) to conduct the iterative computations of explicit deductive reasoning. Our approach significantly enhances the performance of LLMs on the standard mathematical reasoning benchmark, GSM8k, and the Navigate dataset from the BIG-bench dataset. Additionally, we introduce a novel dataset, the Non-Linear Reasoning (NLR) dataset, consisting of 55 unique word problems that target the shortcomings of the next token prediction paradigm of LLMs and require complex non-linear reasoning but only basic arithmetic skills to solve. Our findings demonstrate that the integration of Prolog enables LLMs to achieve high performance on the NLR dataset, which even the most advanced language models (including GPT4) fail to solve using text only.

This report overviews our ongoing work in enriching chain-of-thoughts datasets requiring arithmetical reasoning with the integration of non-parametric components, such as a calculator. We conduct an analysis of prominent relevant datasets such as GSM8K, Ape210K, AQuA-RAT, and MathQA and propose a machine-processable HTML-like format specifically tailored for working with semi-structured chains. By converting the datasets into this unified format, we enable the effective integration of large language models and symbolic systems, empowering them to tackle arithmetical reasoning tasks more efficiently.

Machine reading is a fundamental task for testing the capability of natural language understanding, which is closely related to human cognition in many aspects. With the rising of deep learning techniques, algorithmic models rival human performances on simple QA, and thus increasingly challenging machine reading datasets have been proposed. Though various challenges such as evidence integration and commonsense knowledge have been integrated, one of the fundamental capabilities in human reading, namely logical reasoning, is not fully investigated. We build a comprehensive dataset, named LogiQA, which is sourced from expert-written questions for testing human Logical reasoning. It consists of 8,678 QA instances, covering multiple types of deductive reasoning. Results show that state-of-the-art neural models perform by far worse than human ceiling. Our dataset can also serve as a benchmark for reinvestigating logical AI under the deep learning NLP setting. The dataset is freely available at https://github.com/lgw863/LogiQA-dataset

Since the advent of reasoning-based large language models, many have found great success from distilling reasoning capabilities into student models. Such techniques have significantly bridged the gap between reasoning and standard LLMs on coding tasks. Despite this, much of the progress on distilling reasoning models remains locked behind proprietary datasets or lacks details on data curation, filtering and subsequent training. To address this, we construct a superior supervised fine-tuning (SFT) dataset that we use to achieve state-of-the-art coding capability results in models of various sizes. Our distilled models use only SFT to achieve 61.8% on LiveCodeBench and 24.6% on CodeContests, surpassing alternatives trained with reinforcement learning. We then perform analysis on the data sources used to construct our dataset, the impact of code execution filtering, and the importance of instruction/solution diversity. We observe that execution filtering negatively affected benchmark accuracy, leading us to prioritize instruction diversity over solution correctness. Finally, we also analyze the token efficiency and reasoning patterns utilized by these models. We will open-source these datasets and distilled models to the community.

We present a novel data set, WhoDunIt, to assess the deductive reasoning capabilities of large language models (LLM) within narrative contexts. Constructed from open domain mystery novels and short stories, the dataset challenges LLMs to identify the perpetrator after reading and comprehending the story. To evaluate model robustness, we apply a range of character-level name augmentations, including original names, name swaps, and substitutions with well-known real and/or fictional entities from popular discourse. We further use various prompting styles to investigate the influence of prompting on deductive reasoning accuracy. We conduct evaluation study with state-of-the-art models, specifically GPT-4o, GPT-4-turbo, and GPT-4o-mini, evaluated through multiple trials with majority response selection to ensure reliability. The results demonstrate that while LLMs perform reliably on unaltered texts, accuracy diminishes with certain name substitutions, particularly those with wide recognition. This dataset is publicly available here.

Generating rationales that justify scoring decisions has been a promising way to facilitate explainability in automated scoring systems. However, existing methods do not match the accuracy of classifier-based methods. Plus, the generated rationales often contain hallucinated information. To address these issues, we propose a novel framework capable of generating more faithful rationales and, more importantly, matching performance with classifier-based black-box scoring systems. We first mimic the human assessment process by querying Large Language Models (LLMs) to generate a thought tree. We then summarise intermediate assessment decisions from each thought tree path for creating synthetic rationale data and rationale preference data. Finally, we utilise the generated synthetic data to calibrate LLMs through a two-step training process: supervised fine-tuning and preference optimization. Extensive experimental results demonstrate that our framework achieves a 38% assessment performance improvement in the QWK score compared to prior work while producing higher-quality rationales, as recognised by human evaluators and LLMs. Our work sheds light on the effectiveness of performing preference optimization using synthetic preference data obtained from thought tree paths.

To achieve faithful reasoning that aligns with human expectations, large language models (LLMs) need to ground their reasoning to real-world knowledge (e.g., web facts, math and physical rules). Tools help LLMs access this external knowledge, but there remains challenges for fine-tuning LLM agents (e.g., Toolformer) to invoke tools in multi-step reasoning problems, where inter-connected tool calls require holistic and efficient tool usage planning. In this work, we propose a new method for LLMs to better leverage tools in multi-step reasoning. Our method, Chain-of-Abstraction (CoA), trains LLMs to first decode reasoning chains with abstract placeholders, and then call domain tools to reify each reasoning chain by filling in specific knowledge. This planning with abstract chains enables LLMs to learn more general reasoning strategies, which are robust to shifts of domain knowledge (e.g., math results) relevant to different reasoning questions. It also allows LLMs to perform decoding and calling of external tools in parallel, which avoids the inference delay caused by waiting for tool responses. In mathematical reasoning and Wiki QA domains, we show that our method consistently outperforms previous chain-of-thought and tool-augmented baselines on both in-distribution and out-of-distribution test sets, with an average ~6% absolute QA accuracy improvement. LLM agents trained with our method also show more efficient tool use, with inference speed being on average ~1.4x faster than baseline tool-augmented LLMs.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

Large Language Models are trained on vast amounts of text from the internet, which contains both factual and misleading information about the world. Can language models discern truth from falsehood in this contradicting data? Expanding on the view that LLMs can model different agents producing the corpora, we hypothesize that they can cluster truthful text by modeling a truthful persona: a group of agents that are likely to produce truthful text and share similar features. For example, trustworthy sources like Wikipedia and Science usually use formal writing styles and make consistent claims. By modeling this persona, LLMs can generalize truthfulness beyond the specific contexts in which each agent generated the training text. For example, the model can infer that the agent "Wikipedia" will behave truthfully on topics that were only generated by "Science" because they share a persona. We first show evidence for the persona hypothesis via two observations: (1) we can probe whether a model's answer will be truthful before it is generated; (2) finetuning a model on a set of facts improves its truthfulness on unseen topics. Next, using arithmetics as a synthetic environment, we show that language models can separate true and false statements, and generalize truthfulness across agents; but only if agents in the training data share a truthful generative process that enables the creation of a truthful persona. Overall, our findings suggest that models can exploit hierarchical structures in the data to learn abstract concepts like truthfulness.

OpenAI's recent introduction of Reinforcement Fine-Tuning (RFT) showcases the potential of reasoning foundation model and offers a new paradigm for fine-tuning beyond simple pattern imitation. This technical report presents OpenRFT, our attempt to fine-tune generalist reasoning models for domain-specific tasks under the same settings as RFT. OpenRFT addresses two key challenges of lacking reasoning step data and the limited quantity of training samples, by leveraging the domain-specific samples in three ways: question augmentation, synthesizing reasoning-process data, and few-shot ICL. The evaluation is conducted on SciKnowEval, where OpenRFT achieves notable performance gains with only 100 domain-specific samples for each task. More experimental results will be updated continuously in later versions. Source codes, datasets, and models are disclosed at: https://github.com/ADaM-BJTU/OpenRFT

The derivation of mathematical results in specialised fields using Large Language Models (LLMs) is an emerging research direction that can help identify models' limitations, and potentially support mathematical discovery. In this paper, we leverage a symbolic engine to generate derivations of equations at scale, and investigate the capabilities of LLMs when deriving goal equations from premises. Specifically, we employ in-context learning for GPT and fine-tune a range of T5 models to compare the robustness and generalisation of pre-training strategies to specialised models. Empirical results show that fine-tuned FLAN-T5-large (MathT5) outperforms GPT models on all static and out-of-distribution test sets in terms of absolute performance. However, an in-depth analysis reveals that the fine-tuned models are more sensitive to perturbations involving unseen symbols and (to a lesser extent) changes to equation structure. In addition, we analyse 1.7K equations and over 200 derivations to highlight common reasoning errors such as the inclusion of incorrect, irrelevant, and redundant equations, along with the tendency to skip derivation steps. Finally, we explore the suitability of existing metrics for evaluating mathematical derivations finding evidence that, while they capture general properties such as sensitivity to perturbations, they fail to highlight fine-grained reasoning errors and essential differences between models. Overall, this work demonstrates that training models on synthetic data can improve their mathematical capabilities beyond larger architectures.

Synthetic long-context LLM benchmarks (e.g., "needle-in-the-haystack") test only surface-level retrieval capabilities, but how well can long-context LLMs retrieve, synthesize, and reason over information across book-length inputs? We address this question by creating NoCha, a dataset of 1,001 minimally different pairs of true and false claims about 67 recently-published English fictional books, written by human readers of those books. In contrast to existing long-context benchmarks, our annotators confirm that the largest share of pairs in NoCha require global reasoning over the entire book to verify. Our experiments show that while human readers easily perform this task, it is enormously challenging for all ten long-context LLMs that we evaluate: no open-weight model performs above random chance (despite their strong performance on synthetic benchmarks), while GPT-4o achieves the highest accuracy at 55.8%. Further analysis reveals that (1) on average, models perform much better on pairs that require only sentence-level retrieval vs. global reasoning; (2) model-generated explanations for their decisions are often inaccurate even for correctly-labeled claims; and (3) models perform substantially worse on speculative fiction books that contain extensive world-building. The methodology proposed in NoCha allows for the evolution of the benchmark dataset and the easy analysis of future models.

We present a neuro-symbolic (NeSy) workflow combining a symbolic-based learning technique with a large language model (LLM) agent to generate synthetic data for code comment classification in the C programming language. We also show how generating controlled synthetic data using this workflow fixes some of the notable weaknesses of LLM-based generation and increases the performance of classical machine learning models on the code comment classification task. Our best model, a Neural Network, achieves a Macro-F1 score of 91.412% with an increase of 1.033% after data augmentation.

Large Language Models (LLMs) increasingly rely on prolonged reasoning chains to solve complex tasks. However, this trial-and-error approach often leads to high computational overhead and error propagation, where early mistakes can derail subsequent steps. To address these issues, we introduce Meta-Reasoner, a framework that dynamically optimizes inference-time reasoning by enabling LLMs to "think about how to think." Drawing inspiration from human meta-cognition and dual-process theory, Meta-Reasoner operates as a strategic advisor, decoupling high-level guidance from step-by-step generation. It employs "contextual multi-armed bandits" to iteratively evaluate reasoning progress, and select optimal strategies (e.g., backtrack, clarify ambiguity, restart from scratch, or propose alternative approaches), and reallocates computational resources toward the most promising paths. Our evaluations on mathematical reasoning and puzzles highlight the potential of dynamic reasoning chains to overcome inherent challenges in the LLM reasoning process and also show promise in broader applications, offering a scalable and adaptable solution for reasoning-intensive tasks.

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Scaling model size and training data has led to great advances in the performance of Large Language Models (LLMs). However, the diminishing returns of this approach necessitate alternative methods to improve model capabilities, particularly in tasks requiring advanced reasoning. Large reasoning models, which leverage long chain-of-thoughts, bring unprecedented breakthroughs in problem-solving capabilities but at a substantial deployment cost associated to longer generations. Reducing inference costs is crucial for the economic feasibility, user experience, and environmental sustainability of these models. In this work, we propose to train large reasoning models to reason efficiently. More precisely, we use reinforcement learning (RL) to train reasoning models to dynamically allocate inference-time compute based on task complexity. Our method incentivizes models to minimize unnecessary computational overhead while maintaining accuracy, thereby achieving substantial efficiency gains. It enables the derivation of a family of reasoning models with varying efficiency levels, controlled via a single hyperparameter. Experiments on two open-weight large reasoning models demonstrate significant reductions in inference cost while preserving most of the accuracy.

We present ScienceWorld, a benchmark to test agents' scientific reasoning abilities in a new interactive text environment at the level of a standard elementary school science curriculum. Despite the transformer-based progress seen in question-answering and scientific text processing, we find that current models cannot reason about or explain learned science concepts in novel contexts. For instance, models can easily answer what the conductivity of a known material is but struggle when asked how they would conduct an experiment in a grounded environment to find the conductivity of an unknown material. This begs the question of whether current models are simply retrieving answers by way of seeing a large number of similar examples or if they have learned to reason about concepts in a reusable manner. We hypothesize that agents need to be grounded in interactive environments to achieve such reasoning capabilities. Our experiments provide empirical evidence supporting this hypothesis -- showing that a 1.5 million parameter agent trained interactively for 100k steps outperforms a 11 billion parameter model statically trained for scientific question-answering and reasoning from millions of expert demonstrations.

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data, it is often not enough to have a good approximation of their distribution, as it also requires compliance with constraints that encode essential background knowledge on the problem at hand. In this paper, we address this limitation and show how DGMs for tabular data can be transformed into Constrained Deep Generative Models (C-DGMs), whose generated samples are guaranteed to be compliant with the given constraints. This is achieved by automatically parsing the constraints and transforming them into a Constraint Layer (CL) seamlessly integrated with the DGM. Our extensive experimental analysis with various DGMs and tasks reveals that standard DGMs often violate constraints, some exceeding 95% non-compliance, while their corresponding C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at training time, C-DGMs are able to exploit the background knowledge expressed by the constraints to outperform their standard counterparts with up to 6.5% improvement in utility and detection. Further, we show how our CL does not necessarily need to be integrated at training time, as it can be also used as a guardrail at inference time, still producing some improvements in the overall performance of the models. Finally, we show that our CL does not hinder the sample generation time of the models.

Whether neural networks can learn abstract reasoning or whether they merely rely on superficial statistics is a topic of recent debate. Here, we propose a dataset and challenge designed to probe abstract reasoning, inspired by a well-known human IQ test. To succeed at this challenge, models must cope with various generalisation `regimes' in which the training and test data differ in clearly-defined ways. We show that popular models such as ResNets perform poorly, even when the training and test sets differ only minimally, and we present a novel architecture, with a structure designed to encourage reasoning, that does significantly better. When we vary the way in which the test questions and training data differ, we find that our model is notably proficient at certain forms of generalisation, but notably weak at others. We further show that the model's ability to generalise improves markedly if it is trained to predict symbolic explanations for its answers. Altogether, we introduce and explore ways to both measure and induce stronger abstract reasoning in neural networks. Our freely-available dataset should motivate further progress in this direction.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Large Language Models (LLMs) have shown remarkable capabilities in reasoning, exemplified by the success of OpenAI-o1 and DeepSeek-R1. However, integrating reasoning with external search processes remains challenging, especially for complex multi-hop questions requiring multiple retrieval steps. We propose ReSearch, a novel framework that trains LLMs to Reason with Search via reinforcement learning without using any supervised data on reasoning steps. Our approach treats search operations as integral components of the reasoning chain, where when and how to perform searches is guided by text-based thinking, and search results subsequently influence further reasoning. We train ReSearch on Qwen2.5-7B(-Instruct) and Qwen2.5-32B(-Instruct) models and conduct extensive experiments. Despite being trained on only one dataset, our models demonstrate strong generalizability across various benchmarks. Analysis reveals that ReSearch naturally elicits advanced reasoning capabilities such as reflection and self-correction during the reinforcement learning process.

The development of large language models (LLM) has shown progress on reasoning, though studies have largely considered either English or simple reasoning tasks. To address this, we introduce a multilingual structured reasoning and explanation dataset, termed xSTREET, that covers four tasks across six languages. xSTREET exposes a gap in base LLM performance between English and non-English reasoning tasks. We then propose two methods to remedy this gap, building on the insight that LLMs trained on code are better reasoners. First, at training time, we augment a code dataset with multilingual comments using machine translation while keeping program code as-is. Second, at inference time, we bridge the gap between training and inference by employing a prompt structure that incorporates step-by-step code primitives to derive new facts and find a solution. Our methods show improved multilingual performance on xSTREET, most notably on the scientific commonsense reasoning subtask. Furthermore, the models show no regression on non-reasoning tasks, thus demonstrating our techniques maintain general-purpose abilities.

We explore multi-step reasoning in vision-language models (VLMs). The problem is challenging, as reasoning data consisting of multiple steps of visual and language processing are barely available. To overcome the challenge, we first introduce a least-to-most visual reasoning paradigm, which interleaves steps of decomposing a question into sub-questions and invoking external tools for resolving sub-questions. Based on the paradigm, we further propose a novel data synthesis approach that can automatically create questions and multi-step reasoning paths for an image in a bottom-up manner. Our approach divides the complex synthesis task into a few simple sub-tasks, and (almost entirely) relies on open-sourced models to accomplish the sub-tasks. Therefore, the entire synthesis process is reproducible and cost-efficient, and the synthesized data is quality guaranteed. With the approach, we construct 50k visual reasoning examples. Then, we develop a visual reasoner through supervised fine-tuning, which is capable of generally enhancing the reasoning abilities of a wide range of existing VLMs in a plug-and-play fashion. Extensive experiments indicate that the visual reasoner can consistently and significantly improve four VLMs on four VQA benchmarks. Our code and dataset are available at https://github.com/steven-ccq/VisualReasoner.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

Large Language Models (LLMs) have shown impressive performance in complex reasoning tasks through Chain-of-Thought (CoT) reasoning, allowing models to break down problems into manageable sub-tasks. However, existing CoT evaluation techniques either require annotated CoT data or fall short in accurately assessing intermediate reasoning steps, leading to high rates of false positives. In this paper, we formalize CoT reasoning in LLMs through an information-theoretic lens. Specifically, our framework quantifies the `information gain' at each reasoning step, enabling the identification of failure modes in LLMs without the need for expensive annotated datasets. We demonstrate the efficacy of our approach through extensive experiments on toy and GSM-8K data, where it significantly outperforms existing outcome-based methods by providing more accurate insights into model performance on individual tasks.

Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

While large language models (LLMs) have been thoroughly evaluated for deductive and inductive reasoning, their proficiency in abductive reasoning and holistic rule learning in interactive environments remains less explored. This work introduces RULEARN, a novel benchmark specifically designed to assess the rule-learning ability of LLMs in interactive settings. In RULEARN, agents interact with the environment to gather observations and discern patterns, using these insights to solve problems. To further enhance the rule-learning capabilities of LLM agents within this benchmark, we propose IDEA agent, which integrates Induction, Deduction, and Abduction processes. IDEA agent refines this approach by leveraging a structured reasoning sequence: generating hypotheses through abduction, testing them via deduction, and refining them based on feedback from induction. This sequence enables agents to dynamically establish and apply rules, mimicking human-like reasoning processes. Our evaluation of five representative LLMs indicates that while these models can generate plausible initial hypotheses, they often struggle with strategic interaction within the environment, effective incorporation of feedback, and adaptive refinement of their hypotheses. IDEA agent demonstrates significantly improved performance on the RULEARN benchmark, offering valuable insights for the development of agents capable of human-like rule-learning in real-world scenarios. We will release our code and data.

The Retrieval-Augmented Language Model (RALM) has shown remarkable performance on knowledge-intensive tasks by incorporating external knowledge during inference, which mitigates the factual hallucinations inherited in large language models (LLMs). Despite these advancements, challenges persist in the implementation of RALMs, particularly concerning their reliability and traceability. To be specific, the irrelevant document retrieval may result in unhelpful response generation or even deteriorate the performance of LLMs, while the lack of proper citations in generated outputs complicates efforts to verify the trustworthiness of the models. To this end, we propose a novel self-reasoning framework aimed at improving the reliability and traceability of RALMs, whose core idea is to leverage reasoning trajectories generated by the LLM itself. The framework involves constructing self-reason trajectories with three processes: a relevance-aware process, an evidence-aware selective process, and a trajectory analysis process. We have evaluated our framework across four public datasets (two short-form QA datasets, one long-form QA dataset, and one fact verification dataset) to demonstrate the superiority of our method, which can outperform existing state-of-art models and can achieve comparable performance with GPT-4, while only using 2,000 training samples.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Recent advancements in the field of large language models, particularly through the Chain of Thought (CoT) approach, have demonstrated significant improvements in solving complex problems. However, existing models either tend to sacrifice detailed reasoning for brevity due to user preferences, or require extensive and expensive training data to learn complicated reasoning ability, limiting their potential in solving complex tasks. To bridge this gap, following the concept of scaling test-time, we propose a simple method by encouraging models to adopt a more patient reasoning style without the need of introducing new knowledge or skills. To employ a preference optimization approach, we generate detailed reasoning processes as positive examples and simple answers as negative examples, thereby training the model to favor thoroughness in its responses. Our results demonstrate a performance increase of up to 6.7% on GSM8k with training just on a lightweight dataset.

This paper introduces RuleArena, a novel and challenging benchmark designed to evaluate the ability of large language models (LLMs) to follow complex, real-world rules in reasoning. Covering three practical domains -- airline baggage fees, NBA transactions, and tax regulations -- RuleArena assesses LLMs' proficiency in handling intricate natural language instructions that demand long-context understanding, logical reasoning, and accurate mathematical computation. Two key attributes distinguish RuleArena from traditional rule-based reasoning benchmarks: (1) it extends beyond standard first-order logic representations, and (2) it is grounded in authentic, practical scenarios, providing insights into the suitability and reliability of LLMs for real-world applications. Our findings reveal several notable limitations in LLMs: (1) they struggle to identify and apply the appropriate rules, frequently becoming confused by similar but distinct regulations, (2) they cannot consistently perform accurate mathematical computations, even when they correctly identify the relevant rules, and (3) in general, they perform poorly in the benchmark. These results highlight significant challenges in advancing LLMs' rule-guided reasoning capabilities in real-life applications.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

In math reasoning with large language models (LLMs), fine-tuning data augmentation by query evolution and diverse reasoning paths is empirically verified effective, profoundly narrowing the gap between open-sourced LLMs and cutting-edge proprietary LLMs. In this paper, we conduct an investigation for such data augmentation in math reasoning and are intended to answer: (1) What strategies of data augmentation are more effective; (2) What is the scaling relationship between the amount of augmented data and model performance; and (3) Can data augmentation incentivize generalization to out-of-domain mathematical reasoning tasks? To this end, we create a new dataset, AugGSM8K, by complicating and diversifying the queries from GSM8K and sampling multiple reasoning paths. We obtained a series of LLMs called MuggleMath by fine-tuning on subsets of AugGSM8K. MuggleMath substantially achieves new state-of-the-art on GSM8K (from 54% to 68.4% at the scale of 7B, and from 63.9% to 74.0% at the scale of 13B). A log-linear relationship is presented between MuggleMath's performance and the amount of augmented data. We also find that MuggleMath is weak in out-of-domain math reasoning generalization to MATH. This is attributed to the differences in query distribution between AugGSM8K and MATH which suggest that augmentation on a single benchmark could not help with overall math reasoning performance. Codes and AugGSM8K will be uploaded to https://github.com/OFA-Sys/gsm8k-ScRel.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

Recently, large language models have presented promising results in aiding formal mathematical reasoning. However, their performance is restricted due to the scarcity of formal theorem-proving data, which requires additional effort to be extracted from raw formal language corpora. Meanwhile, a significant amount of human-written formal language corpora remains underutilized. To address this issue, we propose LEAN-GitHub, a dataset consisting of large-scale formal data extracted from almost all Lean 4 repositories on GitHub. After fine-tuning InternLM-math-plus on this dataset, our model achieved accuracies of 48.8% with a single pass and 54.5% with 64 passes on the Lean 4 miniF2F test, surpassing state-of-the-art method at 52%. And it also achieves state-of-the-art on two other Lean 4 benchmarks (ProofNet and Putnam) targeting different fields/levels of math. These results demonstrate that our proposed dataset is beneficial for formal reasoning on a wide range of math topics. We open-source our model at https://GitHub. com/InternLM/InternLM-Math and our data at https://huggingface.co/ datasets/InternLM/Lean-GitHub

Program synthesis with language models (LMs) has unlocked a large set of reasoning abilities; code-tuned LMs have proven adept at generating programs that solve a wide variety of algorithmic symbolic manipulation tasks (e.g. word concatenation). However, not all reasoning tasks are easily expressible as code, e.g. tasks involving commonsense reasoning, moral decision-making, and sarcasm understanding. Our goal is to extend an LM's program synthesis skills to such tasks and evaluate the results via pseudo-programs, namely Python programs where some leaf function calls are left undefined. To that end, we propose, Code Generation and Emulated EXecution (CoGEX). CoGEX works by (1) training LMs to generate their own pseudo-programs, (2) teaching them to emulate their generated program's execution, including those leaf functions, allowing the LM's knowledge to fill in the execution gaps; and (3) using them to search over many programs to find an optimal one. To adapt the CoGEX model to a new task, we introduce a method for performing program search to find a single program whose pseudo-execution yields optimal performance when applied to all the instances of a given dataset. We show that our approach yields large improvements compared to standard in-context learning approaches on a battery of tasks, both algorithmic and soft reasoning. This result thus demonstrates that code synthesis can be applied to a much broader class of problems than previously considered. Our released dataset, fine-tuned models, and implementation can be found at https://github.com/nweir127/CoGEX.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.