Daily Papers

Autoregressive visual generation models typically rely on tokenizers to compress images into tokens that can be predicted sequentially. A fundamental dilemma exists in token representation: discrete tokens enable straightforward modeling with standard cross-entropy loss, but suffer from information loss and tokenizer training instability; continuous tokens better preserve visual details, but require complex distribution modeling, complicating the generation pipeline. In this paper, we propose TokenBridge, which bridges this gap by maintaining the strong representation capacity of continuous tokens while preserving the modeling simplicity of discrete tokens. To achieve this, we decouple discretization from the tokenizer training process through post-training quantization that directly obtains discrete tokens from continuous representations. Specifically, we introduce a dimension-wise quantization strategy that independently discretizes each feature dimension, paired with a lightweight autoregressive prediction mechanism that efficiently model the resulting large token space. Extensive experiments show that our approach achieves reconstruction and generation quality on par with continuous methods while using standard categorical prediction. This work demonstrates that bridging discrete and continuous paradigms can effectively harness the strengths of both approaches, providing a promising direction for high-quality visual generation with simple autoregressive modeling. Project page: https://yuqingwang1029.github.io/TokenBridge.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Autoregressive models have achieved promising results in natural language processing. However, for image generation tasks, they encounter substantial challenges in effectively capturing long-range dependencies, managing computational costs, and most crucially, defining meaningful autoregressive sequences that reflect natural image hierarchies. To address these issues, we present Next-Frequency Image Generation (NFIG), a novel framework that decomposes the image generation process into multiple frequency-guided stages. Our approach first generates low-frequency components to establish global structure with fewer tokens, then progressively adds higher-frequency details, following the natural spectral hierarchy of images. This principled autoregressive sequence not only improves the quality of generated images by better capturing true causal relationships between image components, but also significantly reduces computational overhead during inference. Extensive experiments demonstrate that NFIG achieves state-of-the-art performance with fewer steps, offering a more efficient solution for image generation, with 1.25times speedup compared to VAR-d20 while achieving better performance (FID: 2.81) on the ImageNet-256 benchmark. We hope that our insight of incorporating frequency-domain knowledge to guide autoregressive sequence design will shed light on future research. We will make our code publicly available upon acceptance of the paper.

Autoregressive (AR) models for image generation typically adopt a two-stage paradigm of vector quantization and raster-scan ``next-token prediction", inspired by its great success in language modeling. However, due to the huge modality gap, image autoregressive models may require a systematic reevaluation from two perspectives: tokenizer format and regression direction. In this paper, we introduce the frequency progressive autoregressive (FAR) paradigm and instantiate FAR with the continuous tokenizer. Specifically, we identify spectral dependency as the desirable regression direction for FAR, wherein higher-frequency components build upon the lower one to progressively construct a complete image. This design seamlessly fits the causality requirement for autoregressive models and preserves the unique spatial locality of image data. Besides, we delve into the integration of FAR and the continuous tokenizer, introducing a series of techniques to address optimization challenges and improve the efficiency of training and inference processes. We demonstrate the efficacy of FAR through comprehensive experiments on the ImageNet dataset and verify its potential on text-to-image generation.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

This paper presents Randomized AutoRegressive modeling (RAR) for visual generation, which sets a new state-of-the-art performance on the image generation task while maintaining full compatibility with language modeling frameworks. The proposed RAR is simple: during a standard autoregressive training process with a next-token prediction objective, the input sequence-typically ordered in raster form-is randomly permuted into different factorization orders with a probability r, where r starts at 1 and linearly decays to 0 over the course of training. This annealing training strategy enables the model to learn to maximize the expected likelihood over all factorization orders and thus effectively improve the model's capability of modeling bidirectional contexts. Importantly, RAR preserves the integrity of the autoregressive modeling framework, ensuring full compatibility with language modeling while significantly improving performance in image generation. On the ImageNet-256 benchmark, RAR achieves an FID score of 1.48, not only surpassing prior state-of-the-art autoregressive image generators but also outperforming leading diffusion-based and masked transformer-based methods. Code and models will be made available at https://github.com/bytedance/1d-tokenizer

Sequential dependencies present a fundamental bottleneck in deploying large-scale autoregressive models, particularly for real-time applications. While traditional optimization approaches like pruning and quantization often compromise model quality, recent advances in generation-refinement frameworks demonstrate that this trade-off can be significantly mitigated. This survey presents a comprehensive taxonomy of generation-refinement frameworks, analyzing methods across autoregressive sequence tasks. We categorize methods based on their generation strategies (from simple n-gram prediction to sophisticated draft models) and refinement mechanisms (including single-pass verification and iterative approaches). Through systematic analysis of both algorithmic innovations and system-level implementations, we examine deployment strategies across computing environments and explore applications spanning text, images, and speech generation. This systematic examination of both theoretical frameworks and practical implementations provides a foundation for future research in efficient autoregressive decoding.

Autoregressive models, despite their commendable performance in a myriad of generative tasks, face challenges stemming from their inherently sequential structure. Inference on these models, by design, harnesses a temporal dependency, where the current token's probability distribution is conditioned on preceding tokens. This inherent characteristic severely impedes computational efficiency during inference as a typical inference request can require more than thousands of tokens, where generating each token requires a load of entire model weights, making the inference more memory-bound. The large overhead becomes profound in real deployment where requests arrive randomly, necessitating various generation lengths. Existing solutions, such as dynamic batching and concurrent instances, introduce significant response delays and bandwidth contention, falling short of achieving optimal latency and throughput. To address these shortcomings, we propose Flover -- a temporal fusion framework for efficiently inferring multiple requests in parallel. We deconstruct the general generation pipeline into pre-processing and token generation, and equip the framework with a dedicated work scheduler for fusing the generation process temporally across all requests. By orchestrating the token-level parallelism, Flover exhibits optimal hardware efficiency and significantly spares the system resources. By further employing a fast buffer reordering algorithm that allows memory eviction of finished tasks, it brings over 11x inference speedup on GPT and 16x on LLAMA compared to the cutting-edge solutions provided by NVIDIA FasterTransformer. Crucially, by leveraging the advanced tensor parallel technique, Flover proves efficacious across diverse computational landscapes, from single-GPU setups to distributed scenarios, thereby offering robust performance optimization that adapts to variable use cases.

Autoregressive (AR) modeling, known for its next-token prediction paradigm, underpins state-of-the-art language and visual generative models. Traditionally, a ``token'' is treated as the smallest prediction unit, often a discrete symbol in language or a quantized patch in vision. However, the optimal token definition for 2D image structures remains an open question. Moreover, AR models suffer from exposure bias, where teacher forcing during training leads to error accumulation at inference. In this paper, we propose xAR, a generalized AR framework that extends the notion of a token to an entity X, which can represent an individual patch token, a cell (a ktimes k grouping of neighboring patches), a subsample (a non-local grouping of distant patches), a scale (coarse-to-fine resolution), or even a whole image. Additionally, we reformulate discrete token classification as continuous entity regression, leveraging flow-matching methods at each AR step. This approach conditions training on noisy entities instead of ground truth tokens, leading to Noisy Context Learning, which effectively alleviates exposure bias. As a result, xAR offers two key advantages: (1) it enables flexible prediction units that capture different contextual granularity and spatial structures, and (2) it mitigates exposure bias by avoiding reliance on teacher forcing. On ImageNet-256 generation benchmark, our base model, xAR-B (172M), outperforms DiT-XL/SiT-XL (675M) while achieving 20times faster inference. Meanwhile, xAR-H sets a new state-of-the-art with an FID of 1.24, running 2.2times faster than the previous best-performing model without relying on vision foundation modules (\eg, DINOv2) or advanced guidance interval sampling.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become increasingly larger. Speculative decoding employs a "draft and then verify" mechanism to allow multiple tokens to be generated in one step, realizing lossless acceleration. Existing methods mainly adopt fixed heuristic draft structures, which fail to adapt to different situations to maximize the acceptance length during verification. To alleviate this dilemma, we proposed OPT-Tree, an algorithm to construct adaptive and scalable draft trees. It searches the optimal tree structure that maximizes the mathematical expectation of the acceptance length in each decoding step. Experimental results reveal that OPT-Tree outperforms the existing draft structures and achieves a speed-up ratio of up to 3.2 compared with autoregressive decoding. If the draft model is powerful enough and the node budget is sufficient, it can generate more than ten tokens in a single step. Our code is available at https://github.com/Jikai0Wang/OPT-Tree.

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special cases of ARDMs under mild assumptions. ARDMs are simple to implement and easy to train. Unlike standard ARMs, they do not require causal masking of model representations, and can be trained using an efficient objective similar to modern probabilistic diffusion models that scales favourably to highly-dimensional data. At test time, ARDMs support parallel generation which can be adapted to fit any given generation budget. We find that ARDMs require significantly fewer steps than discrete diffusion models to attain the same performance. Finally, we apply ARDMs to lossless compression, and show that they are uniquely suited to this task. Contrary to existing approaches based on bits-back coding, ARDMs obtain compelling results not only on complete datasets, but also on compressing single data points. Moreover, this can be done using a modest number of network calls for (de)compression due to the model's adaptable parallel generation.

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous Autoregressive Models (CAMs) can suffer from a decline in generation quality over extended sequences due to error accumulation during inference. We introduce a novel method to address this issue by injecting random noise into the input embeddings during training. This procedure makes the model robust against varying error levels at inference. We further reduce error accumulation through an inference procedure that introduces low-level noise. Experiments on musical audio generation show that CAM substantially outperforms existing autoregressive and non-autoregressive approaches while preserving audio quality over extended sequences. This work paves the way for generating continuous embeddings in a purely autoregressive setting, opening new possibilities for real-time and interactive generative applications.

Speculative decoding has been widely used to accelerate autoregressive (AR) text generation. However, its effectiveness in visual AR models remains limited due to token selection ambiguity, where multiple tokens receive similarly low probabilities, reducing acceptance rates. While dynamic tree drafting has been proposed to improve speculative decoding, we show that it fails to mitigate token selection ambiguity, resulting in shallow draft trees and suboptimal acceleration. To address this, we introduce LANTERN++, a novel framework that integrates static tree drafting with a relaxed acceptance condition, allowing drafts to be selected independently of low-confidence predictions. This enables deeper accepted sequences, improving decoding efficiency while preserving image quality. Extensive experiments on state-of-the-art visual AR models demonstrate that LANTERN++ significantly accelerates inference, achieving up to times 2.56 speedup over standard AR decoding while maintaining high image quality.

Much recent effort has been invested in non-autoregressive neural machine translation, which appears to be an efficient alternative to state-of-the-art autoregressive machine translation on modern GPUs. In contrast to the latter, where generation is sequential, the former allows generation to be parallelized across target token positions. Some of the latest non-autoregressive models have achieved impressive translation quality-speed tradeoffs compared to autoregressive baselines. In this work, we reexamine this tradeoff and argue that autoregressive baselines can be substantially sped up without loss in accuracy. Specifically, we study autoregressive models with encoders and decoders of varied depths. Our extensive experiments show that given a sufficiently deep encoder, a single-layer autoregressive decoder can substantially outperform strong non-autoregressive models with comparable inference speed. We show that the speed disadvantage for autoregressive baselines compared to non-autoregressive methods has been overestimated in three aspects: suboptimal layer allocation, insufficient speed measurement, and lack of knowledge distillation. Our results establish a new protocol for future research toward fast, accurate machine translation. Our code is available at https://github.com/jungokasai/deep-shallow.

Autoregressive models have shown remarkable success in image generation by adapting sequential prediction techniques from language modeling. However, applying these approaches to images requires discretizing continuous pixel data through vector quantization methods like VQ-VAE. To alleviate the quantization errors that existed in VQ-VAE, recent works tend to use larger codebooks. However, this will accordingly expand vocabulary size, complicating the autoregressive modeling task. This paper aims to find a way to enjoy the benefits of large codebooks without making autoregressive modeling more difficult. Through empirical investigation, we discover that tokens with similar codeword representations produce similar effects on the final generated image, revealing significant redundancy in large codebooks. Based on this insight, we propose to predict tokens from coarse to fine (CTF), realized by assigning the same coarse label for similar tokens. Our framework consists of two stages: (1) an autoregressive model that sequentially predicts coarse labels for each token in the sequence, and (2) an auxiliary model that simultaneously predicts fine-grained labels for all tokens conditioned on their coarse labels. Experiments on ImageNet demonstrate our method's superior performance, achieving an average improvement of 59 points in Inception Score compared to baselines. Notably, despite adding an inference step, our approach achieves faster sampling speeds.

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

Model selection is a critical step in time series forecasting, traditionally requiring extensive performance evaluations across various datasets. Meta-learning approaches aim to automate this process, but they typically depend on pre-constructed performance matrices, which are costly to build. In this work, we propose to leverage Large Language Models (LLMs) as a lightweight alternative for model selection. Our method eliminates the need for explicit performance matrices by utilizing the inherent knowledge and reasoning capabilities of LLMs. Through extensive experiments with LLaMA, GPT and Gemini, we demonstrate that our approach outperforms traditional meta-learning techniques and heuristic baselines, while significantly reducing computational overhead. These findings underscore the potential of LLMs in efficient model selection for time series forecasting.

The two dominant approaches to neural text generation are fully autoregressive models, using serial beam search decoding, and non-autoregressive models, using parallel decoding with no output dependencies. This work proposes an autoregressive model with sub-linear parallel time generation. Noting that conditional random fields with bounded context can be decoded in parallel, we propose an efficient cascaded decoding approach for generating high-quality output. To parameterize this cascade, we introduce a Markov transformer, a variant of the popular fully autoregressive model that allows us to simultaneously decode with specific autoregressive context cutoffs. This approach requires only a small modification from standard autoregressive training, while showing competitive accuracy/speed tradeoff compared to existing methods on five machine translation datasets.

The sequential nature of modern LLMs makes them expensive and slow, and speculative sampling has proven to be an effective solution to this problem. Methods like EAGLE perform autoregression at the feature level, reusing top-layer features from the target model to achieve better results than vanilla speculative sampling. A growing trend in the LLM community is scaling up training data to improve model intelligence without increasing inference costs. However, we observe that scaling up data provides limited improvements for EAGLE. We identify that this limitation arises from EAGLE's feature prediction constraints. In this paper, we introduce EAGLE-3, which abandons feature prediction in favor of direct token prediction and replaces reliance on top-layer features with multi-layer feature fusion via a technique named training-time test. These improvements significantly enhance performance and enable the draft model to fully benefit from scaling up training data. Our experiments include both chat models and reasoning models, evaluated on five tasks. The results show that EAGLE-3 achieves a speedup ratio up to 6.5x, with about 1.4x improvement over EAGLE-2. The code is available at https://github.com/SafeAILab/EAGLE.

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

Autoregressive (AR) models have achieved state-of-the-art performance in text and image generation but suffer from slow generation due to the token-by-token process. We ask an ambitious question: can a pre-trained AR model be adapted to generate outputs in just one or two steps? If successful, this would significantly advance the development and deployment of AR models. We notice that existing works that try to speed up AR generation by generating multiple tokens at once fundamentally cannot capture the output distribution due to the conditional dependencies between tokens, limiting their effectiveness for few-step generation. To address this, we propose Distilled Decoding (DD), which uses flow matching to create a deterministic mapping from Gaussian distribution to the output distribution of the pre-trained AR model. We then train a network to distill this mapping, enabling few-step generation. DD doesn't need the training data of the original AR model, making it more practical.We evaluate DD on state-of-the-art image AR models and present promising results on ImageNet-256. For VAR, which requires 10-step generation, DD enables one-step generation (6.3times speed-up), with an acceptable increase in FID from 4.19 to 9.96. For LlamaGen, DD reduces generation from 256 steps to 1, achieving an 217.8times speed-up with a comparable FID increase from 4.11 to 11.35. In both cases, baseline methods completely fail with FID>100. DD also excels on text-to-image generation, reducing the generation from 256 steps to 2 for LlamaGen with minimal FID increase from 25.70 to 28.95. As the first work to demonstrate the possibility of one-step generation for image AR models, DD challenges the prevailing notion that AR models are inherently slow, and opens up new opportunities for efficient AR generation. The project website is at https://imagination-research.github.io/distilled-decoding.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.

Efficient inference in large language models (LLMs) has become a critical focus as their scale and complexity grow. Traditional autoregressive decoding, while effective, suffers from computational inefficiencies due to its sequential token generation process. Speculative decoding addresses this bottleneck by introducing a two-stage framework: drafting and verification. A smaller, efficient model generates a preliminary draft, which is then refined by a larger, more sophisticated model. This paper provides a comprehensive survey of speculative decoding methods, categorizing them into draft-centric and model-centric approaches. We discuss key ideas associated with each method, highlighting their potential for scaling LLM inference. This survey aims to guide future research in optimizing speculative decoding and its integration into real-world LLM applications.

Autoregressive (AR) modeling has achieved remarkable success in natural language processing by enabling models to generate text with coherence and contextual understanding through next token prediction. Recently, in image generation, VAR proposes scale-wise autoregressive modeling, which extends the next token prediction to the next scale prediction, preserving the 2D structure of images. However, VAR encounters two primary challenges: (1) its complex and rigid scale design limits generalization in next scale prediction, and (2) the generator's dependence on a discrete tokenizer with the same complex scale structure restricts modularity and flexibility in updating the tokenizer. To address these limitations, we introduce FlowAR, a general next scale prediction method featuring a streamlined scale design, where each subsequent scale is simply double the previous one. This eliminates the need for VAR's intricate multi-scale residual tokenizer and enables the use of any off-the-shelf Variational AutoEncoder (VAE). Our simplified design enhances generalization in next scale prediction and facilitates the integration of Flow Matching for high-quality image synthesis. We validate the effectiveness of FlowAR on the challenging ImageNet-256 benchmark, demonstrating superior generation performance compared to previous methods. Codes will be available at https://github.com/OliverRensu/FlowAR.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

We introduce AiM, an autoregressive (AR) image generative model based on Mamba architecture. AiM employs Mamba, a novel state-space model characterized by its exceptional performance for long-sequence modeling with linear time complexity, to supplant the commonly utilized Transformers in AR image generation models, aiming to achieve both superior generation quality and enhanced inference speed. Unlike existing methods that adapt Mamba to handle two-dimensional signals via multi-directional scan, AiM directly utilizes the next-token prediction paradigm for autoregressive image generation. This approach circumvents the need for extensive modifications to enable Mamba to learn 2D spatial representations. By implementing straightforward yet strategically targeted modifications for visual generative tasks, we preserve Mamba's core structure, fully exploiting its efficient long-sequence modeling capabilities and scalability. We provide AiM models in various scales, with parameter counts ranging from 148M to 1.3B. On the ImageNet1K 256*256 benchmark, our best AiM model achieves a FID of 2.21, surpassing all existing AR models of comparable parameter counts and demonstrating significant competitiveness against diffusion models, with 2 to 10 times faster inference speed. Code is available at https://github.com/hp-l33/AiM

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Inference from large autoregressive models like Transformers is slow - decoding K tokens takes K serial runs of the model. In this work we introduce speculative decoding - an algorithm to sample from autoregressive models faster without any changes to the outputs, by computing several tokens in parallel. At the heart of our approach lie the observations that (1) hard language-modeling tasks often include easier subtasks that can be approximated well by more efficient models, and (2) using speculative execution and a novel sampling method, we can make exact decoding from the large models faster, by running them in parallel on the outputs of the approximation models, potentially generating several tokens concurrently, and without changing the distribution. Our method can accelerate existing off-the-shelf models without retraining or architecture changes. We demonstrate it on T5-XXL and show a 2X-3X acceleration compared to the standard T5X implementation, with identical outputs.

The performance of large language models (LLMs) is closely linked to their underlying size, leading to ever-growing networks and hence slower inference. Speculative decoding has been proposed as a technique to accelerate autoregressive generation, leveraging a fast draft model to propose candidate tokens, which are then verified in parallel based on their likelihood under the target model. While this approach guarantees to reproduce the target output, it incurs a substantial penalty: many high-quality draft tokens are rejected, even when they represent objectively valid continuations. Indeed, we show that even powerful draft models such as GPT-4o, as well as human text cannot achieve high acceptance rates under the standard verification scheme. This severely limits the speedup potential of current speculative decoding methods, as an early rejection becomes overwhelmingly likely when solely relying on alignment of draft and target. We thus ask the following question: Can we adapt verification to recognize correct, but non-aligned replies? To this end, we draw inspiration from the LLM-as-a-judge framework, which demonstrated that LLMs are able to rate answers in a versatile way. We carefully design a dataset to elicit the same capability in the target model by training a compact module on top of the embeddings to produce ``judgements" of the current continuation. We showcase our strategy on the Llama-3.1 family, where our 8b/405B-Judge achieves a speedup of 9x over Llama-405B, while maintaining its quality on a large range of benchmarks. These benefits remain present even in optimized inference frameworks, where our method reaches up to 141 tokens/s for 8B/70B-Judge and 129 tokens/s for 8B/405B on 2 and 8 H100s respectively.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Autoregressive sampling from large language models has led to state-of-the-art results in several natural language tasks. However, autoregressive sampling generates tokens one at a time making it slow, and even prohibitive in certain tasks. One way to speed up sampling is speculative decoding: use a small model to sample a draft (block or sequence of tokens), and then score all tokens in the draft by the large language model in parallel. A subset of the tokens in the draft are accepted (and the rest rejected) based on a statistical method to guarantee that the final output follows the distribution of the large model. In this work, we provide a principled understanding of speculative decoding through the lens of optimal transport (OT) with membership cost. This framework can be viewed as an extension of the well-known maximal-coupling problem. This new formulation enables us to generalize the speculative decoding method to allow for a set of k candidates at the token-level, which leads to an improved optimal membership cost. We show that the optimal draft selection algorithm (transport plan) can be computed via linear programming, whose best-known runtime is exponential in k. We then propose a valid draft selection algorithm whose acceptance probability is (1-1/e)-optimal multiplicatively. Moreover, it can be computed in time almost linear with size of domain of a single token. Using this new draft selection algorithm, we develop a new autoregressive sampling algorithm called SpecTr, which provides speedup in decoding while ensuring that there is no quality degradation in the decoded output. We experimentally demonstrate that for state-of-the-art large language models, the proposed approach achieves a wall clock speedup of 2.13X, a further 1.37X speedup over speculative decoding on standard benchmarks.

Despite the crucial importance of accelerating text generation in large language models (LLMs) for efficiently producing content, the sequential nature of this process often leads to high inference latency, posing challenges for real-time applications. Various techniques have been proposed and developed to address these challenges and improve efficiency. This paper presents a comprehensive survey of accelerated generation techniques in autoregressive language models, aiming to understand the state-of-the-art methods and their applications. We categorize these techniques into several key areas: speculative decoding, early exiting mechanisms, and non-autoregressive methods. We discuss each category's underlying principles, advantages, limitations, and recent advancements. Through this survey, we aim to offer insights into the current landscape of techniques in LLMs and provide guidance for future research directions in this critical area of natural language processing.

To mitigate the high inference latency stemming from autoregressive decoding in Large Language Models (LLMs), Speculative Decoding has emerged as a novel decoding paradigm for LLM inference. In each decoding step, this method first efficiently drafts several future tokens and then verifies them in parallel. Unlike autoregressive decoding, Speculative Decoding facilitates the simultaneous decoding of multiple tokens per step, thereby accelerating inference. This paper presents a comprehensive overview and analysis of this promising decoding paradigm. We begin by providing a formal definition and formulation of Speculative Decoding. Then, we organize in-depth discussions on its key facets, including current leading techniques, the challenges faced, and potential future directions in this field. We aim for this work to serve as a catalyst for further research on Speculative Decoding, ultimately contributing to more efficient LLM inference.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Autoregressive models have emerged as a powerful approach for visual generation but suffer from slow inference speed due to their sequential token-by-token prediction process. In this paper, we propose a simple yet effective approach for parallelized autoregressive visual generation that improves generation efficiency while preserving the advantages of autoregressive modeling. Our key insight is that parallel generation depends on visual token dependencies-tokens with weak dependencies can be generated in parallel, while strongly dependent adjacent tokens are difficult to generate together, as their independent sampling may lead to inconsistencies. Based on this observation, we develop a parallel generation strategy that generates distant tokens with weak dependencies in parallel while maintaining sequential generation for strongly dependent local tokens. Our approach can be seamlessly integrated into standard autoregressive models without modifying the architecture or tokenizer. Experiments on ImageNet and UCF-101 demonstrate that our method achieves a 3.6x speedup with comparable quality and up to 9.5x speedup with minimal quality degradation across both image and video generation tasks. We hope this work will inspire future research in efficient visual generation and unified autoregressive modeling. Project page: https://epiphqny.github.io/PAR-project.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Autoregressive modeling has been a huge success in the field of natural language processing (NLP). Recently, autoregressive models have emerged as a significant area of focus in computer vision, where they excel in producing high-quality visual content. Autoregressive models in NLP typically operate on subword tokens. However, the representation strategy in computer vision can vary in different levels, i.e., pixel-level, token-level, or scale-level, reflecting the diverse and hierarchical nature of visual data compared to the sequential structure of language. This survey comprehensively examines the literature on autoregressive models applied to vision. To improve readability for researchers from diverse research backgrounds, we start with preliminary sequence representation and modeling in vision. Next, we divide the fundamental frameworks of visual autoregressive models into three general sub-categories, including pixel-based, token-based, and scale-based models based on the strategy of representation. We then explore the interconnections between autoregressive models and other generative models. Furthermore, we present a multi-faceted categorization of autoregressive models in computer vision, including image generation, video generation, 3D generation, and multi-modal generation. We also elaborate on their applications in diverse domains, including emerging domains such as embodied AI and 3D medical AI, with about 250 related references. Finally, we highlight the current challenges to autoregressive models in vision with suggestions about potential research directions. We have also set up a Github repository to organize the papers included in this survey at: https://github.com/ChaofanTao/Autoregressive-Models-in-Vision-Survey.

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to fine next-scale prediction. In this paper, we show that this scale-wise autoregressive framework can be effectively decoupled into intra-scale modeling, which captures local spatial dependencies within each scale, and inter-scale modeling, which models cross-scale relationships progressively from coarse-to-fine scales. This decoupling structure allows to rebuild VAR in a more computationally efficient manner. Specifically, for intra-scale modeling -- crucial for generating high-fidelity images -- we retain the original bidirectional self-attention design to ensure comprehensive modeling; for inter-scale modeling, which semantically connects different scales but is computationally intensive, we apply linear-complexity mechanisms like Mamba to substantially reduce computational overhead. We term this new framework M-VAR. Extensive experiments demonstrate that our method outperforms existing models in both image quality and generation speed. For example, our 1.5B model, with fewer parameters and faster inference speed, outperforms the largest VAR-d30-2B. Moreover, our largest model M-VAR-d32 impressively registers 1.78 FID on ImageNet 256times256 and outperforms the prior-art autoregressive models LlamaGen/VAR by 0.4/0.19 and popular diffusion models LDM/DiT by 1.82/0.49, respectively. Code is avaiable at https://github.com/OliverRensu/MVAR.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

To tackle the high inference latency exhibited by autoregressive language models, previous studies have proposed an early-exiting framework that allocates adaptive computation paths for each token based on the complexity of generating the subsequent token. However, we observed several shortcomings, including performance degradation caused by a state copying mechanism or numerous exit paths, and sensitivity to exit confidence thresholds. Consequently, we propose a Fast and Robust Early-Exiting (FREE) framework, which incorporates a shallow-deep module and a synchronized parallel decoding. Our framework enables faster inference by synchronizing the decoding process of the current token with previously stacked early-exited tokens. Furthermore, as parallel decoding allows us to observe predictions from both shallow and deep models, we present a novel adaptive threshold estimator that exploits a Beta mixture model to determine suitable confidence thresholds. We empirically demonstrated the superiority of our proposed framework on extensive generation tasks.

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

The autoregressive nature of conventional large language models (LLMs) inherently limits inference speed, as tokens are generated sequentially. While speculative and parallel decoding techniques attempt to mitigate this, they face limitations: either relying on less accurate smaller models for generation or failing to fully leverage the base LLM's representations. We introduce a novel architecture, Tandem transformers, to address these issues. This architecture uniquely combines (1) a small autoregressive model and (2) a large model operating in block mode (processing multiple tokens simultaneously). The small model's predictive accuracy is substantially enhanced by granting it attention to the large model's richer representations. On the PaLM2 pretraining dataset, a tandem of PaLM2-Bison and PaLM2-Gecko demonstrates a 3.3% improvement in next-token prediction accuracy over a standalone PaLM2-Gecko, offering a 1.16x speedup compared to a PaLM2-Otter model with comparable downstream performance. We further incorporate the tandem model within the speculative decoding (SPEED) framework where the large model validates tokens from the small model. This ensures that the Tandem of PaLM2-Bison and PaLM2-Gecko achieves substantial speedup (around 1.14x faster than using vanilla PaLM2-Gecko in SPEED) while maintaining identical downstream task accuracy.

Scene text recognition (STR) methods have struggled to attain high accuracy and fast inference speed. Autoregressive (AR)-based models implement the recognition in a character-by-character manner, showing superiority in accuracy but with slow inference speed. Alternatively, parallel decoding (PD)-based models infer all characters in a single decoding pass, offering faster inference speed but generally worse accuracy. We first present an empirical study of AR decoding in STR, and discover that the AR decoder not only models linguistic context, but also provides guidance on visual context perception. Consequently, we propose Context Perception Parallel Decoder (CPPD) to predict the character sequence in a PD pass. CPPD devises a character counting module to infer the occurrence count of each character, and a character ordering module to deduce the content-free reading order and placeholders. Meanwhile, the character prediction task associates the placeholders with characters. They together build a comprehensive recognition context. We construct a series of CPPD models and also plug the proposed modules into existing STR decoders. Experiments on both English and Chinese benchmarks demonstrate that the CPPD models achieve highly competitive accuracy while running approximately 8x faster than their AR-based counterparts. Moreover, the plugged models achieve significant accuracy improvements. Code is at https://github.com/PaddlePaddle/PaddleOCR/blob/dygraph/doc/doc_en/algorithm_rec_cppd_en.md{this https URL}.

To combat the memory bandwidth-bound nature of autoregressive LLM inference, previous research has proposed the speculative decoding framework. To perform speculative decoding, a small draft model proposes candidate continuations of the input sequence, that are then verified in parallel by the base model. One way to specify the draft model, as used in the recent Medusa decoding framework, is as a collection of light-weight heads, called draft heads, that operate on the base model's hidden states. To date, all existing draft heads have been sequentially independent, meaning that they speculate tokens in the candidate continuation independently of any preceding tokens in the candidate continuation. In this work, we propose Hydra heads, a sequentially dependent, drop-in replacement for standard draft heads that significantly improves speculation accuracy. Decoding with Hydra heads improves throughput compared to Medusa decoding with standard draft heads. We further explore the design space of Hydra head training objectives and architectures, and propose a carefully-tuned Hydra head recipe, which we call Hydra++, that improves decoding throughput by 1.31x and 2.71x compared to Medusa decoding and autoregressive decoding, respectively. Overall, Hydra heads are a simple intervention on standard draft heads that significantly improve the end-to-end speed of draft head based speculative decoding.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Auto-Regressive (AR) models have recently gained prominence in image generation, often matching or even surpassing the performance of diffusion models. However, one major limitation of AR models is their sequential nature, which processes tokens one at a time, slowing down generation compared to models like GANs or diffusion-based methods that operate more efficiently. While speculative decoding has proven effective for accelerating LLMs by generating multiple tokens in a single forward, its application in visual AR models remains largely unexplored. In this work, we identify a challenge in this setting, which we term token selection ambiguity, wherein visual AR models frequently assign uniformly low probabilities to tokens, hampering the performance of speculative decoding. To overcome this challenge, we propose a relaxed acceptance condition referred to as LANTERN that leverages the interchangeability of tokens in latent space. This relaxation restores the effectiveness of speculative decoding in visual AR models by enabling more flexible use of candidate tokens that would otherwise be prematurely rejected. Furthermore, by incorporating a total variation distance bound, we ensure that these speed gains are achieved without significantly compromising image quality or semantic coherence. Experimental results demonstrate the efficacy of our method in providing a substantial speed-up over speculative decoding. In specific, compared to a na\"ive application of the state-of-the-art speculative decoding, LANTERN increases speed-ups by 1.75times and 1.76times, as compared to greedy decoding and random sampling, respectively, when applied to LlamaGen, a contemporary visual AR model.

The widespread adoption of scalable mobile sensing has led to large amounts of time series data for real-world applications. A fundamental application is multivariate time series forecasting (MTSF), which aims to predict future time series values based on historical observations. Existing MTSF methods suffer from limited parameterization and small-scale training data. Recently, Large language models (LLMs) have been introduced in time series, which achieve promising forecasting performance but incur heavy computational costs. To solve these challenges, we propose TimeCMA, an LLM-empowered framework for time series forecasting with cross-modality alignment. We design a dual-modality encoding module with two branches, where the time series encoding branch extracts relatively low-quality yet pure embeddings of time series through an inverted Transformer. In addition, the LLM-empowered encoding branch wraps the same time series as prompts to obtain high-quality yet entangled prompt embeddings via a Pre-trained LLM. Then, we design a cross-modality alignment module to retrieve high-quality and pure time series embeddings from the prompt embeddings. Moreover, we develop a time series forecasting module to decode the aligned embeddings while capturing dependencies among multiple variables for forecasting. Notably, we tailor the prompt to encode sufficient temporal information into a last token and design the last token embedding storage to reduce computational costs. Extensive experiments on real data offer insight into the accuracy and efficiency of the proposed framework.

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

We introduce AutoGluon-TimeSeries - an open-source AutoML library for probabilistic time series forecasting. Focused on ease of use and robustness, AutoGluon-TimeSeries enables users to generate accurate point and quantile forecasts with just 3 lines of Python code. Built on the design philosophy of AutoGluon, AutoGluon-TimeSeries leverages ensembles of diverse forecasting models to deliver high accuracy within a short training time. AutoGluon-TimeSeries combines both conventional statistical models, machine-learning based forecasting approaches, and ensembling techniques. In our evaluation on 29 benchmark datasets, AutoGluon-TimeSeries demonstrates strong empirical performance, outperforming a range of forecasting methods in terms of both point and quantile forecast accuracy, and often even improving upon the best-in-hindsight combination of prior methods.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Sequential Recommendation (SeqRec) aims to predict the next item by capturing sequential patterns from users' historical interactions, playing a crucial role in many real-world recommender systems. However, existing approaches predominantly adopt a direct forward computation paradigm, where the final hidden state of the sequence encoder serves as the user representation. We argue that this inference paradigm, due to its limited computational depth, struggles to model the complex evolving nature of user preferences and lacks a nuanced understanding of long-tail items, leading to suboptimal performance. To address this issue, we propose ReaRec, the first inference-time computing framework for recommender systems, which enhances user representations through implicit multi-step reasoning. Specifically, ReaRec autoregressively feeds the sequence's last hidden state into the sequential recommender while incorporating special reasoning position embeddings to decouple the original item encoding space from the multi-step reasoning space. Moreover, we introduce two lightweight reasoning-based learning methods, Ensemble Reasoning Learning (ERL) and Progressive Reasoning Learning (PRL), to further effectively exploit ReaRec's reasoning potential. Extensive experiments on five public real-world datasets and different SeqRec architectures demonstrate the generality and effectiveness of our proposed ReaRec. Remarkably, post-hoc analyses reveal that ReaRec significantly elevates the performance ceiling of multiple sequential recommendation backbones by approximately 30\%-50\%. Thus, we believe this work can open a new and promising avenue for future research in inference-time computing for sequential recommendation.

Autoregressive decoding is the only part of sequence-to-sequence models that prevents them from massive parallelization at inference time. Non-autoregressive models enable the decoder to generate all output symbols independently in parallel. We present a novel non-autoregressive architecture based on connectionist temporal classification and evaluate it on the task of neural machine translation. Unlike other non-autoregressive methods which operate in several steps, our model can be trained end-to-end. We conduct experiments on the WMT English-Romanian and English-German datasets. Our models achieve a significant speedup over the autoregressive models, keeping the translation quality comparable to other non-autoregressive models.

Autoregressive Large Language Models (e.g., LLaMa, GPTs) are omnipresent achieving remarkable success in language understanding and generation. However, such impressive capability typically comes with a substantial model size, which presents significant challenges for autoregressive token-by-token generation. To mitigate computation overload incurred during generation, several early-exit and layer-dropping strategies have been proposed. Despite some promising success due to the redundancy across LLMs layers on metrics like Rough-L/BLUE, our careful knowledge-intensive evaluation unveils issues such as generation collapse, hallucination of wrong facts, and noticeable performance drop even at the trivial exit ratio of 10-15% of layers. We attribute these errors primarily to ineffective handling of the KV cache through state copying during early-exit. In this work, we observed the saturation of computationally expensive feed-forward blocks of LLM layers and proposed FFN-SkipLLM, which is a novel fine-grained skip strategy of autoregressive LLMs. More specifically, FFN-SkipLLM is an input-adaptive feed-forward skipping strategy that can skip 25-30% of FFN blocks of LLMs with marginal change in performance on knowledge-intensive generation tasks without any requirement to handle KV cache. Our extensive experiments and ablation across benchmarks like MT-Bench, Factoid-QA, and variable-length text summarization illustrate how our simple and ease-at-use method can facilitate faster autoregressive decoding.

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

Can meta-learning discover generic ways of processing time series (TS) from a diverse dataset so as to greatly improve generalization on new TS coming from different datasets? This work provides positive evidence to this using a broad meta-learning framework which we show subsumes many existing meta-learning algorithms. Our theoretical analysis suggests that residual connections act as a meta-learning adaptation mechanism, generating a subset of task-specific parameters based on a given TS input, thus gradually expanding the expressive power of the architecture on-the-fly. The same mechanism is shown via linearization analysis to have the interpretation of a sequential update of the final linear layer. Our empirical results on a wide range of data emphasize the importance of the identified meta-learning mechanisms for successful zero-shot univariate forecasting, suggesting that it is viable to train a neural network on a source TS dataset and deploy it on a different target TS dataset without retraining, resulting in performance that is at least as good as that of state-of-practice univariate forecasting models.

Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.

We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard raster-scan "next-token prediction". This simple, intuitive methodology allows autoregressive (AR) transformers to learn visual distributions fast and generalize well: VAR, for the first time, makes AR models surpass diffusion transformers in image generation. On ImageNet 256x256 benchmark, VAR significantly improve AR baseline by improving Frechet inception distance (FID) from 18.65 to 1.80, inception score (IS) from 80.4 to 356.4, with around 20x faster inference speed. It is also empirically verified that VAR outperforms the Diffusion Transformer (DiT) in multiple dimensions including image quality, inference speed, data efficiency, and scalability. Scaling up VAR models exhibits clear power-law scaling laws similar to those observed in LLMs, with linear correlation coefficients near -0.998 as solid evidence. VAR further showcases zero-shot generalization ability in downstream tasks including image in-painting, out-painting, and editing. These results suggest VAR has initially emulated the two important properties of LLMs: Scaling Laws and zero-shot task generalization. We have released all models and codes to promote the exploration of AR/VAR models for visual generation and unified learning.

Large language models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their widespread application is hindered by the resource-intensive decoding process. To address this challenge, current approaches have incorporated additional decoding heads to enable parallel prediction of multiple subsequent tokens, thereby achieving inference acceleration. Nevertheless, the accuracy of these decoding heads falls short of the auto-regressive decoding approach. In light of these limitations, we propose Chimera, a novel framework specifically designed for speculative sampling. Within this framework, we introduce a lightweight draft model that effectively utilizes previously generated tokens to predict subsequent words. To ensure both accuracy and efficiency, we present two strategies within the lightweight draft model. Firstly, we focus on capturing short-range dependencies at the bottom layer. Secondly, we leverage the readily available representations from the original LLM.Through empirical evaluation on the Vicuna and LlaMA-2 series, Chimera demonstrates impressive results, achieving an average latency speedup ratio of 2.7x compared to the vanilla auto-regressive decoding approach. This highlights the potential of our proposed framework in significantly improving the efficiency of large language models during the decoding process.

Large language model (LLM) decoding involves generating a sequence of tokens based on a given context, where each token is predicted one at a time using the model's learned probabilities. The typical autoregressive decoding method requires a separate forward pass through the model for each token generated, which is computationally inefficient and poses challenges for deploying LLMs in latency-sensitive scenarios. The main limitations of current decoding methods stem from their inefficiencies and resource demands. Existing approaches either necessitate fine-tuning smaller models, which is resource-intensive, or rely on fixed retrieval schemes to construct drafts for the next tokens, which lack adaptability and fail to generalize across different models and contexts. To address these issues, we introduce a novel methodology called ADED, which accelerates LLM decoding without requiring fine-tuning. Our approach involves an adaptive draft-verification process that evolves over time to improve efficiency. We utilize a tri-gram matrix-based LLM representation to dynamically approximate the output distribution of the LLM, allowing the model to adjust to changing token probabilities during the decoding process. Additionally, we implement a draft construction mechanism that effectively balances exploration and exploitation, ensuring that the drafts generated are both diverse and close to the true output distribution of the LLM. The importance of this design lies in its ability to optimize the draft distribution adaptively, leading to faster and more accurate decoding. Through extensive experiments on various benchmark datasets and LLM architectures, we demonstrate that ADED significantly accelerates the decoding process while maintaining high accuracy, making it suitable for deployment in a wide range of practical applications.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

Deployment of autoregressive large language models (LLMs) is costly, and as these models increase in size, the associated costs will become even more considerable. Consequently, different methods have been proposed to accelerate the token generation process and reduce costs. Speculative decoding (SD) is among the most promising approaches to speed up the LLM decoding process by verifying multiple tokens in parallel and using an auxiliary smaller draft model to generate the possible tokens. In SD, usually, one draft model is used to serve a specific target model; however, in practice, LLMs are diverse, and we might need to deal with many target models or more than one target model simultaneously. In this scenario, it is not clear which draft model should be used for which target model, and searching among different draft models or training customized draft models can further increase deployment costs. In this paper, we first introduce a novel multi-target scenario for the deployment of draft models for faster inference. Then, we present a novel, more efficient sorted speculative decoding mechanism that outperforms regular baselines in multi-target settings. We evaluated our method on Spec-Bench in different settings, including base models such as Vicuna 7B, 13B, and LLama Chat 70B. Our results suggest that our draft models perform better than baselines for multiple target models at the same time.

The recent emergence of Large Language Models based on the Transformer architecture has enabled dramatic advancements in the field of Natural Language Processing. However, these models have long inference latency, which limits their deployment and makes them prohibitively expensive for various real-time applications. The inference latency is further exacerbated by autoregressive generative tasks, as models need to run iteratively to generate tokens sequentially without leveraging token-level parallelization. To address this, we propose Big Little Decoder (BiLD), a framework that can improve inference efficiency and latency for a wide range of text generation applications. The BiLD framework contains two models with different sizes that collaboratively generate text. The small model runs autoregressively to generate text with a low inference cost, and the large model is only invoked occasionally to refine the small model's inaccurate predictions in a non-autoregressive manner. To coordinate the small and large models, BiLD introduces two simple yet effective policies: (1) the fallback policy that determines when to hand control over to the large model; and (2) the rollback policy that determines when the large model needs to correct the small model's inaccurate predictions. To evaluate our framework across different tasks and models, we apply BiLD to various text generation scenarios encompassing machine translation on IWSLT 2017 De-En and WMT 2014 De-En, and summarization on XSUM and CNN/DailyMail. On an NVIDIA T4 GPU, our framework achieves a speedup of up to 2.12x speedup with minimal generation quality degradation. Furthermore, our framework is fully plug-and-play and can be applied without any modifications in the training process or model architecture. Our code is open-sourced

This paper focuses on developing modern, efficient, lightweight models for dense predictions while trading off parameters, FLOPs, and performance. Inverted Residual Block (IRB) serves as the infrastructure for lightweight CNNs, but no counterpart has been recognized by attention-based studies. This work rethinks lightweight infrastructure from efficient IRB and effective components of Transformer from a unified perspective, extending CNN-based IRB to attention-based models and abstracting a one-residual Meta Mobile Block (MMB) for lightweight model design. Following simple but effective design criterion, we deduce a modern Inverted Residual Mobile Block (iRMB) and build a ResNet-like Efficient MOdel (EMO) with only iRMB for down-stream tasks. Extensive experiments on ImageNet-1K, COCO2017, and ADE20K benchmarks demonstrate the superiority of our EMO over state-of-the-art methods, e.g., EMO-1M/2M/5M achieve 71.5, 75.1, and 78.4 Top-1 that surpass equal-order CNN-/Attention-based models, while trading-off the parameter, efficiency, and accuracy well: running 2.8-4.0x faster than EdgeNeXt on iPhone14.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.

Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex distributions, yet can be trained efficiently using exact maximum likelihood, unlike GANs or VAEs. Our proposed model is autoregressive and uses LSTMs to enable arbitrarily long time-dependencies. Importantly, is is also causal, meaning that each pose in the output sequence is generated without access to poses or control inputs from future time steps; this absence of algorithmic latency is important for interactive applications with real-time motion control. The approach can in principle be applied to any type of motion since it does not make restrictive, task-specific assumptions regarding the motion or the character morphology. We evaluate the models on motion-capture datasets of human and quadruped locomotion. Objective and subjective results show that randomly-sampled motion from the proposed method outperforms task-agnostic baselines and attains a motion quality close to recorded motion capture.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer.

Existing approaches to neural machine translation condition each output word on previously generated outputs. We introduce a model that avoids this autoregressive property and produces its outputs in parallel, allowing an order of magnitude lower latency during inference. Through knowledge distillation, the use of input token fertilities as a latent variable, and policy gradient fine-tuning, we achieve this at a cost of as little as 2.0 BLEU points relative to the autoregressive Transformer network used as a teacher. We demonstrate substantial cumulative improvements associated with each of the three aspects of our training strategy, and validate our approach on IWSLT 2016 English-German and two WMT language pairs. By sampling fertilities in parallel at inference time, our non-autoregressive model achieves near-state-of-the-art performance of 29.8 BLEU on WMT 2016 English-Romanian.

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

We present Autoregressive Representation Alignment (ARRA), a new training framework that unlocks global-coherent text-to-image generation in autoregressive LLMs without architectural changes. Unlike prior work that requires complex architectural redesigns, ARRA aligns LLM hidden states with visual representations from external visual foundational models via a global visual alignment loss and a hybrid token, <HYBNEXT>. This token enforces dual constraints: local next-token prediction and global semantic distillation, enabling LLMs to implicitly learn spatial and contextual coherence while retaining their original autoregressive paradigm. Extensive experiments validate ARRA's plug-and-play versatility. When training from text-generation-only LLMs or random initialization, ARRA reduces FID by 25.5% (MIMIC-CXR), 8.8% (DeepEyeNet), and 7.5% (ImageNet) for advanced autoregressive LLMs like Chameleon and LlamaGen, all without framework modifications. For domain adaption, ARRA aligns general-purpose LLMs with specialized models (e.g., BioMedCLIP), achieving an 18.6% FID reduction over direct fine-tuning on medical imaging (MIMIC-CXR). By demonstrating that training objective redesign -- not just architectural innovation -- can resolve cross-modal global coherence challenges, ARRA offers a complementary paradigm for advancing autoregressive models. Code and models will be released to advance autoregressive image generation.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

Transformers have gained popularity in time series forecasting for their ability to capture long-sequence interactions. However, their high memory and computing requirements pose a critical bottleneck for long-term forecasting. To address this, we propose TSMixer, a lightweight neural architecture exclusively composed of multi-layer perceptron (MLP) modules for multivariate forecasting and representation learning on patched time series. Inspired by MLP-Mixer's success in computer vision, we adapt it for time series, addressing challenges and introducing validated components for enhanced accuracy. This includes a novel design paradigm of attaching online reconciliation heads to the MLP-Mixer backbone, for explicitly modeling the time-series properties such as hierarchy and channel-correlations. We also propose a novel Hybrid channel modeling and infusion of a simple gating approach to effectively handle noisy channel interactions and generalization across diverse datasets. By incorporating these lightweight components, we significantly enhance the learning capability of simple MLP structures, outperforming complex Transformer models with minimal computing usage. Moreover, TSMixer's modular design enables compatibility with both supervised and masked self-supervised learning methods, making it a promising building block for time-series Foundation Models. TSMixer outperforms state-of-the-art MLP and Transformer models in forecasting by a considerable margin of 8-60%. It also outperforms the latest strong benchmarks of Patch-Transformer models (by 1-2%) with a significant reduction in memory and runtime (2-3X). The source code of our model is officially released as PatchTSMixer in the HuggingFace. Model: https://huggingface.co/docs/transformers/main/en/model_doc/patchtsmixer Examples: https://github.com/ibm/tsfm/#notebooks-links

This paper introduces a novel training methodology that enables a small Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at: https://github.com/AGPatriota/ALGA-R/.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

Deep models have demonstrated remarkable performance in time series forecasting. However, due to the partially-observed nature of real-world applications, solely focusing on the target of interest, so-called endogenous variables, is usually insufficient to guarantee accurate forecasting. Notably, a system is often recorded into multiple variables, where the exogenous variables can provide valuable external information for endogenous variables. Thus, unlike well-established multivariate or univariate forecasting paradigms that either treat all the variables equally or ignore exogenous information, this paper focuses on a more practical setting: time series forecasting with exogenous variables. We propose a novel approach, TimeXer, to ingest external information to enhance the forecasting of endogenous variables. With deftly designed embedding layers, TimeXer empowers the canonical Transformer with the ability to reconcile endogenous and exogenous information, where patch-wise self-attention and variate-wise cross-attention are used simultaneously. Moreover, global endogenous tokens are learned to effectively bridge the causal information underlying exogenous series into endogenous temporal patches. Experimentally, TimeXer achieves consistent state-of-the-art performance on twelve real-world forecasting benchmarks and exhibits notable generality and scalability. Code is available at this repository: https://github.com/thuml/TimeXer.

Table-to-text generation refers to generating a descriptive text from a key-value table. Traditional autoregressive methods, though can generate text with high fluency, suffer from low coverage and poor faithfulness problems. To mitigate these problems, we propose a novel Skeleton-based two-stage method that combines both Autoregressive and Non-Autoregressive generations (SANA). Our approach includes: (1) skeleton generation with an autoregressive pointer network to select key tokens from the source table; (2) edit-based non-autoregressive generation model to produce texts via iterative insertion and deletion operations. By integrating hard constraints from the skeleton, the non-autoregressive model improves the generation's coverage over the source table and thus enhances its faithfulness. We conduct automatic and human evaluations on both WikiPerson and WikiBio datasets. Experimental results demonstrate that our method outperforms the previous state-of-the-art methods in both automatic and human evaluation, especially on coverage and faithfulness. In particular, we achieve PARENT-T recall of 99.47 in WikiPerson, improving over the existing best results by more than 10 points.

A multivariate time series refers to observations of two or more variables taken from a device or a system simultaneously over time. There is an increasing need to monitor multivariate time series and detect anomalies in real time to ensure proper system operation and good service quality. It is also highly desirable to have a lightweight anomaly detection system that considers correlations between different variables, adapts to changes in the pattern of the multivariate time series, offers immediate responses, and provides supportive information regarding detection results based on unsupervised learning and online model training. In the past decade, many multivariate time series anomaly detection approaches have been introduced. However, they are unable to offer all the above-mentioned features. In this paper, we propose RoLA, a real-time online lightweight anomaly detection system for multivariate time series based on a divide-and-conquer strategy, parallel processing, and the majority rule. RoLA employs multiple lightweight anomaly detectors to monitor multivariate time series in parallel, determine the correlations between variables dynamically on the fly, and then jointly detect anomalies based on the majority rule in real time. To demonstrate the performance of RoLA, we conducted an experiment based on a public dataset provided by the FerryBox of the One Ocean Expedition. The results show that RoLA provides satisfactory detection accuracy and lightweight performance.

High-frequency trading (HFT) represents a pivotal and intensely competitive domain within the financial markets. The velocity and accuracy of data processing exert a direct influence on profitability, underscoring the significance of this field. The objective of this work is to optimise the real-time processing of data in high-frequency trading algorithms. The dynamic feature selection mechanism is responsible for monitoring and analysing market data in real time through clustering and feature weight analysis, with the objective of automatically selecting the most relevant features. This process employs an adaptive feature extraction method, which enables the system to respond and adjust its feature set in a timely manner when the data input changes, thus ensuring the efficient utilisation of data. The lightweight neural networks are designed in a modular fashion, comprising fast convolutional layers and pruning techniques that facilitate the expeditious completion of data processing and output prediction. In contrast to conventional deep learning models, the neural network architecture has been specifically designed to minimise the number of parameters and computational complexity, thereby markedly reducing the inference time. The experimental results demonstrate that the model is capable of maintaining consistent performance in the context of varying market conditions, thereby illustrating its advantages in terms of processing speed and revenue enhancement.

Time series forecasting has been a widely explored task of great importance in many applications. However, it is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model and the limited and noisy time series. In this work, we propose to address the time series forecasting problem with generative modeling and propose a bidirectional variational auto-encoder (BVAE) equipped with diffusion, denoise, and disentanglement, namely D3VAE. Specifically, a coupled diffusion probabilistic model is proposed to augment the time series data without increasing the aleatoric uncertainty and implement a more tractable inference process with BVAE. To ensure the generated series move toward the true target, we further propose to adapt and integrate the multiscale denoising score matching into the diffusion process for time series forecasting. In addition, to enhance the interpretability and stability of the prediction, we treat the latent variable in a multivariate manner and disentangle them on top of minimizing total correlation. Extensive experiments on synthetic and real-world data show that D3VAE outperforms competitive algorithms with remarkable margins. Our implementation is available at https://github.com/PaddlePaddle/PaddleSpatial/tree/main/research/D3VAE.

It is desirable but challenging to generate content-rich long videos in the scale of minutes. Autoregressive large language models (LLMs) have achieved great success in generating coherent and long sequences of tokens in the domain of natural language processing, while the exploration of autoregressive LLMs for video generation is limited to generating short videos of several seconds. In this work, we conduct a deep analysis of the challenges that prevent autoregressive LLM-based video generators from generating long videos. Based on the observations and analysis, we propose Loong, a new autoregressive LLM-based video generator that can generate minute-long videos. Specifically, we model the text tokens and video tokens as a unified sequence for autoregressive LLMs and train the model from scratch. We propose progressive short-to-long training with a loss re-weighting scheme to mitigate the loss imbalance problem for long video training. We further investigate inference strategies, including video token re-encoding and sampling strategies, to diminish error accumulation during inference. Our proposed Loong can be trained on 10-second videos and be extended to generate minute-level long videos conditioned on text prompts, as demonstrated by the results. More samples are available at: https://epiphqny.github.io/Loong-video.

The success of autoregressive (AR) language models in text generation has inspired the computer vision community to adopt Large Language Models (LLMs) for image generation. However, considering the essential differences between text and image modalities, the design space of language models for image generation remains underexplored. We observe that image tokens exhibit greater randomness compared to text tokens, which presents challenges when training with token prediction. Nevertheless, AR models demonstrate their potential by effectively learning patterns even from a seemingly suboptimal optimization problem. Our analysis also reveals that while all models successfully grasp the importance of local information in image generation, smaller models struggle to capture the global context. In contrast, larger models showcase improved capabilities in this area, helping to explain the performance gains achieved when scaling up model size. We further elucidate the design space of language models for vision generation, including tokenizer choice, model choice, model scalability, vocabulary design, and sampling strategy through extensive comparative experiments. Our work is the first to analyze the optimization behavior of language models in vision generation, and we believe it can inspire more effective designs when applying LMs to other domains. Finally, our elucidated language model for image generation, termed as ELM, achieves state-of-the-art performance on the ImageNet 256*256 benchmark. The code is available at https://github.com/Pepperlll/LMforImageGeneration.git.

Stock movement prediction, a fundamental task in financial time-series forecasting, requires identifying and retrieving critical influencing factors from vast amounts of time-series data. However, existing text-trained or numeric similarity-based retrieval methods fall short in handling complex financial analysis. To address this, we propose the first retrieval-augmented generation (RAG) framework for financial time-series forecasting, featuring three key innovations: a fine-tuned 1B parameter large language model (StockLLM) as the backbone, a novel candidate selection method leveraging LLM feedback, and a training objective that maximizes similarity between queries and historically significant sequences. This enables our retriever, FinSeer, to uncover meaningful patterns while minimizing noise in complex financial data. We also construct new datasets integrating financial indicators and historical stock prices to train FinSeer and ensure robust evaluation. Experimental results demonstrate that our RAG framework outperforms bare StockLLM and random retrieval, highlighting its effectiveness, while FinSeer surpasses existing retrieval methods, achieving an 8\% higher accuracy on BIGDATA22 and retrieving more impactful sequences. This work underscores the importance of tailored retrieval models in financial forecasting and provides a novel framework for future research.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

Among adversarial attacks against sequential recommender systems, model extraction attacks represent a method to attack sequential recommendation models without prior knowledge. Existing research has primarily concentrated on the adversary's execution of black-box attacks through data-free model extraction. However, a significant gap remains in the literature concerning the development of surrogate models by adversaries with access to few-shot raw data (10\% even less). That is, the challenge of how to construct a surrogate model with high functional similarity within the context of few-shot data scenarios remains an issue that requires resolution.This study addresses this gap by introducing a novel few-shot model extraction framework against sequential recommenders, which is designed to construct a superior surrogate model with the utilization of few-shot data. The proposed few-shot model extraction framework is comprised of two components: an autoregressive augmentation generation strategy and a bidirectional repair loss-facilitated model distillation procedure. Specifically, to generate synthetic data that closely approximate the distribution of raw data, autoregressive augmentation generation strategy integrates a probabilistic interaction sampler to extract inherent dependencies and a synthesis determinant signal module to characterize user behavioral patterns. Subsequently, bidirectional repair loss, which target the discrepancies between the recommendation lists, is designed as auxiliary loss to rectify erroneous predictions from surrogate models, transferring knowledge from the victim model to the surrogate model effectively. Experiments on three datasets show that the proposed few-shot model extraction framework yields superior surrogate models.

In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or major architectural changes. We identify the SequenceMatch-chi^2 divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models.

The growth of the Machine-Learning-As-A-Service (MLaaS) market has highlighted clients' data privacy and security issues. Private inference (PI) techniques using cryptographic primitives offer a solution but often have high computation and communication costs, particularly with non-linear operators like ReLU. Many attempts to reduce ReLU operations exist, but they may need heuristic threshold selection or cause substantial accuracy loss. This work introduces AutoReP, a gradient-based approach to lessen non-linear operators and alleviate these issues. It automates the selection of ReLU and polynomial functions to speed up PI applications and introduces distribution-aware polynomial approximation (DaPa) to maintain model expressivity while accurately approximating ReLUs. Our experimental results demonstrate significant accuracy improvements of 6.12% (94.31%, 12.9K ReLU budget, CIFAR-10), 8.39% (74.92%, 12.9K ReLU budget, CIFAR-100), and 9.45% (63.69%, 55K ReLU budget, Tiny-ImageNet) over current state-of-the-art methods, e.g., SNL. Morever, AutoReP is applied to EfficientNet-B2 on ImageNet dataset, and achieved 75.55% accuracy with 176.1 times ReLU budget reduction.

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, model weights, and data will be released.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to predict multiple tokens, which are then verified in parallel by the larger target model. However, the limited capacity of the draft model often necessitates tree-based sampling to improve prediction accuracy, where multiple candidates are generated at each step. We identify a key limitation in this approach: the candidates at the same step are derived from the same representation, limiting diversity and reducing overall effectiveness. To address this, we propose Jakiro, leveraging Mixture of Experts (MoE), where independent experts generate diverse predictions, effectively decoupling correlations among candidates. Furthermore, we introduce a hybrid inference strategy, combining autoregressive decoding for initial tokens with parallel decoding for subsequent stages, and enhance the latter with contrastive mechanism in features to improve accuracy. Our method significantly boosts prediction accuracy and achieves higher inference speedups. Extensive experiments across diverse models validate the effectiveness and robustness of our approach, establishing a new SOTA in speculative decoding. Our codes are available at https://github.com/haiduo/Jakiro.

Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and applicability issues. An alternative is to use fully latent temporal models which untie frame synthesis and temporal dynamics. However, no such model for stochastic video prediction has been proposed in the literature yet, due to design and training difficulties. In this paper, we overcome these difficulties by introducing a novel stochastic temporal model whose dynamics are governed in a latent space by a residual update rule. This first-order scheme is motivated by discretization schemes of differential equations. It naturally models video dynamics as it allows our simpler, more interpretable, latent model to outperform prior state-of-the-art methods on challenging datasets.

In this note we examine the autoregressive generalization of the FNet algorithm, in which self-attention layers from the standard Transformer architecture are substituted with a trivial sparse-uniformsampling procedure based on Fourier transforms. Using the Wikitext-103 benchmark, we demonstratethat FNetAR retains state-of-the-art performance (25.8 ppl) on the task of causal language modelingcompared to a Transformer-XL baseline (24.2 ppl) with only half the number self-attention layers,thus providing further evidence for the superfluity of deep neural networks with heavily compoundedattention mechanisms. The autoregressive Fourier transform could likely be used for parameterreduction on most Transformer-based time-series prediction models.

With the advance of diffusion models, today's video generation has achieved impressive quality. To extend the generation length and facilitate real-world applications, a majority of video diffusion models (VDMs) generate videos in an autoregressive manner, i.e., generating subsequent clips conditioned on the last frame(s) of the previous clip. However, existing autoregressive VDMs are highly inefficient and redundant: The model must re-compute all the conditional frames that are overlapped between adjacent clips. This issue is exacerbated when the conditional frames are extended autoregressively to provide the model with long-term context. In such cases, the computational demands increase significantly (i.e., with a quadratic complexity w.r.t. the autoregression step). In this paper, we propose Ca2-VDM, an efficient autoregressive VDM with Causal generation and Cache sharing. For causal generation, it introduces unidirectional feature computation, which ensures that the cache of conditional frames can be precomputed in previous autoregression steps and reused in every subsequent step, eliminating redundant computations. For cache sharing, it shares the cache across all denoising steps to avoid the huge cache storage cost. Extensive experiments demonstrated that our Ca2-VDM achieves state-of-the-art quantitative and qualitative video generation results and significantly improves the generation speed. Code is available at https://github.com/Dawn-LX/CausalCache-VDM

Historically, LLMs have been trained using either autoregressive (AR) or masked language modeling (MLM) objectives, with AR models gaining dominance in recent years. However, AR models are inherently incapable of masked infilling, which is the ability to predict masked tokens between past and future context. In contrast, MLM models suffer from intrinsic computational inefficiencies during both training and inference that hinder their scalability. This work introduces MARIA (Masked and Autoregressive Infilling Architecture), a novel approach that leverages the strengths of both paradigms to achieve state-of-the-art masked infilling performance. MARIA combines a pre-trained MLM and AR model by training a linear decoder that takes their concatenated hidden states as input. This minimal modification enables the AR model to perform infilling while retaining its inherent advantages in terms of faster inference with KV caching. Our results demonstrate that MARIA significantly outperforms existing methods, namely discrete diffusion models, on masked infilling tasks.

Large language models (LLMs) commonly employ autoregressive generation during inference, leading to high memory bandwidth demand and consequently extended latency. To mitigate this inefficiency, we present Bi-directional Tuning for lossless Acceleration (BiTA), an innovative method expediting LLMs via streamlined semi-autoregressive generation and draft verification. Inspired by the concept of prompt tuning, we enhance LLMs with a parameter-efficient design called bi-directional tuning for the capability in semi-autoregressive generation. Employing efficient tree-based decoding, the models perform draft candidate generation and verification in parallel, ensuring outputs identical to their autoregressive counterparts under greedy sampling. BiTA serves as a lightweight plug-in module, seamlessly boosting the inference efficiency of existing LLMs without requiring additional assistance models or incurring significant extra memory costs. Applying the proposed BiTA, LLaMA-2-70B-Chat achieves a 2.7times speedup on the MT-Bench benchmark. Extensive experiments confirm our method surpasses state-of-the-art acceleration techniques.

This research aims to accelerate the inference speed of large language models (LLMs) with billions of parameters. We propose Smart Parallel Auto-Correct dEcoding (SPACE), an innovative approach designed for achieving lossless acceleration of LLMs. By integrating semi-autoregressive inference and speculative decoding capabilities, SPACE uniquely enables autoregressive LLMs to parallelize token generation and verification. This is realized through a specialized semi-autoregressive supervised fine-tuning process that equips existing LLMs with the ability to simultaneously predict multiple tokens. Additionally, an auto-correct decoding algorithm facilitates the simultaneous generation and verification of token sequences within a single model invocation. Through extensive experiments on a range of LLMs, SPACE has demonstrated inference speedup ranging from 2.7x-4.0x on HumanEval-X while maintaining output quality.

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

We introduce SessionRec, a novel next-session prediction paradigm (NSPP) for generative sequential recommendation, addressing the fundamental misalignment between conventional next-item prediction paradigm (NIPP) and real-world recommendation scenarios. Unlike NIPP's item-level autoregressive generation that contradicts actual session-based user interactions, our framework introduces a session-aware representation learning through hierarchical sequence aggregation (intra/inter-session), reducing attention computation complexity while enabling implicit modeling of massive negative interactions, and a session-based prediction objective that better captures users' diverse interests through multi-item recommendation in next sessions. Moreover, we found that incorporating a rank loss for items within the session under the next session prediction paradigm can significantly improve the ranking effectiveness of generative sequence recommendation models. We also verified that SessionRec exhibits clear power-law scaling laws similar to those observed in LLMs. Extensive experiments conducted on public datasets and online A/B test in Meituan App demonstrate the effectiveness of SessionRec. The proposed paradigm establishes new foundations for developing industrial-scale generative recommendation systems through its model-agnostic architecture and computational efficiency.

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

Autoregressive Predictive Coding (APC), as a self-supervised objective, has enjoyed success in learning representations from large amounts of unlabeled data, and the learned representations are rich for many downstream tasks. However, the connection between low self-supervised loss and strong performance in downstream tasks remains unclear. In this work, we propose Vector-Quantized Autoregressive Predictive Coding (VQ-APC), a novel model that produces quantized representations, allowing us to explicitly control the amount of information encoded in the representations. By studying a sequence of increasingly limited models, we reveal the constituents of the learned representations. In particular, we confirm the presence of information with probing tasks, while showing the absence of information with mutual information, uncovering the model's preference in preserving speech information as its capacity becomes constrained. We find that there exists a point where phonetic and speaker information are amplified to maximize a self-supervised objective. As a byproduct, the learned codes for a particular model capacity correspond well to English phones.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

Autoregressive decoding limits the efficiency of transformers for Machine Translation (MT). The community proposed specific network architectures and learning-based methods to solve this issue, which are expensive and require changes to the MT model, trading inference speed at the cost of the translation quality. In this paper, we propose to address the problem from the point of view of decoding algorithms, as a less explored but rather compelling direction. We propose to reframe the standard greedy autoregressive decoding of MT with a parallel formulation leveraging Jacobi and Gauss-Seidel fixed-point iteration methods for fast inference. This formulation allows to speed up existing models without training or modifications while retaining translation quality. We present three parallel decoding algorithms and test them on different languages and models showing how the parallelization introduces a speedup up to 38% w.r.t. the standard autoregressive decoding and nearly 2x when scaling the method on parallel resources. Finally, we introduce a decoding dependency graph visualizer (DDGviz) that let us see how the model has learned the conditional dependence between tokens and inspect the decoding procedure.

We propose Speculative Decoding (SpecDec), for the first time ever, to formally study exploiting the idea of speculative execution to accelerate autoregressive (AR) decoding. Speculative Decoding has two innovations: Spec-Drafter -- an independent model specially optimized for efficient and accurate drafting -- and Spec-Verification -- a reliable method for verifying the drafted tokens efficiently in the decoding paradigm. Experimental results on various seq2seq tasks including machine translation and abstractive summarization show our approach can achieve around 5times speedup for the popular Transformer architectures with comparable generation quality to beam search decoding, refreshing the impression that the draft-then-verify paradigm introduces only 1.4timessim2times speedup. In addition to the remarkable speedup, we also demonstrate 3 additional advantages of SpecDec, revealing its practical value for accelerating generative models in real-world applications. Our models and codes are available at https://github.com/hemingkx/SpecDec.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

We empirically study autoregressive pre-training from videos. To perform our study, we construct a series of autoregressive video models, called Toto. We treat videos as sequences of visual tokens and train transformer models to autoregressively predict future tokens. Our models are pre-trained on a diverse dataset of videos and images comprising over 1 trillion visual tokens. We explore different architectural, training, and inference design choices. We evaluate the learned visual representations on a range of downstream tasks including image recognition, video classification, object tracking, and robotics. Our results demonstrate that, despite minimal inductive biases, autoregressive pre-training leads to competitive performance across all benchmarks. Finally, we find that scaling our video models results in similar scaling curves to those seen in language models, albeit with a different rate. More details at https://brjathu.github.io/toto/

Large Language Models (LLMs) inherently use autoregressive decoding, which lacks parallelism in inference and results in significantly slow inference speeds, especially when hardware parallel accelerators and memory bandwidth are not fully utilized. In this work, we propose Amphista, a speculative decoding algorithm that adheres to a non-autoregressive decoding paradigm. Owing to the increased parallelism, our method demonstrates higher efficiency in inference compared to autoregressive methods. Specifically, Amphista models an Auto-embedding Block capable of parallel inference, incorporating bi-directional attention to enable interaction between different drafting heads. Additionally, Amphista implements Staged Adaptation Layers to facilitate the transition of semantic information from the base model's autoregressive inference to the drafting heads' non-autoregressive speculation, thereby achieving paradigm transformation and feature fusion. We conduct a series of experiments on a suite of Vicuna models using MT-Bench and Spec-Bench. For the Vicuna 33B model, Amphista achieves up to 2.75times and 1.40times wall-clock acceleration compared to vanilla autoregressive decoding and Medusa, respectively, while preserving lossless generation quality.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

The conventional evaluation protocols on machine learning models rely heavily on a labeled, i.i.d-assumed testing dataset, which is not often present in real world applications. The Automated Model Evaluation (AutoEval) shows an alternative to this traditional workflow, by forming a proximal prediction pipeline of the testing performance without the presence of ground-truth labels. Despite its recent successes, the AutoEval frameworks still suffer from an overconfidence issue, substantial storage and computational cost. In that regard, we propose a novel measure -- Meta-Distribution Energy (MDE) -- that allows the AutoEval framework to be both more efficient and effective. The core of the MDE is to establish a meta-distribution statistic, on the information (energy) associated with individual samples, then offer a smoother representation enabled by energy-based learning. We further provide our theoretical insights by connecting the MDE with the classification loss. We provide extensive experiments across modalities, datasets and different architectural backbones to validate MDE's validity, together with its superiority compared with prior approaches. We also prove MDE's versatility by showing its seamless integration with large-scale models, and easy adaption to learning scenarios with noisy- or imbalanced- labels. Code and data are available: https://github.com/pengr/Energy_AutoEval

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

Speculative decoding is an inference-acceleration method for large language models (LLMs) where a small language model generates a draft-token sequence which is further verified by the target LLM in parallel. Recent works have advanced this method by establishing a draft-token tree, achieving superior performance over a single-sequence speculative decoding. However, those works independently generate tokens at each level of the tree, not leveraging the tree's entire diversifiability. Besides, their empirical superiority has been shown for fixed length of sequences, implicitly granting more computational resource to LLM for the tree-based methods. None of the existing works has conducted empirical studies with fixed target computational budgets despite its importance to resource-bounded devices. We present Recursive Speculative Decoding (RSD), a novel tree-based method that samples draft tokens without replacement and maximizes the diversity of the tree. During RSD's drafting, the tree is built by either Gumbel-Top-k trick that draws tokens without replacement in parallel or Stochastic Beam Search that samples sequences without replacement while early-truncating unlikely draft sequences and reducing the computational cost of LLM. We empirically evaluate RSD with Llama 2 and OPT models, showing that RSD outperforms the baseline methods, consistently for fixed draft sequence length and in most cases for fixed computational budgets at LLM.

Autoregressive Large Language Models (LLMs) have achieved impressive performance in language tasks but face two significant bottlenecks: (1) quadratic complexity in the attention module as the number of tokens increases, and (2) limited efficiency due to the sequential processing nature of autoregressive LLMs during generation. While linear attention and speculative decoding offer potential solutions, their applicability and synergistic potential for enhancing autoregressive LLMs remain uncertain. We conduct the first comprehensive study on the efficacy of existing linear attention methods for autoregressive LLMs, integrating them with speculative decoding. We introduce an augmentation technique for linear attention that ensures compatibility with speculative decoding, enabling more efficient training and serving of LLMs. Extensive experiments and ablation studies involving seven existing linear attention models and five encoder/decoder-based LLMs consistently validate the effectiveness of our augmented linearized LLMs. Notably, our approach achieves up to a 6.67 reduction in perplexity on the LLaMA model and up to a 2times speedup during generation compared to prior linear attention methods. Codes and models are available at https://github.com/GATECH-EIC/Linearized-LLM.

Speculative Decoding has gained popularity as an effective technique for accelerating the auto-regressive inference process of Large Language Models (LLMs). However, Speculative Decoding entirely relies on the availability of efficient draft models, which are often lacking for many existing language models due to a stringent constraint of vocabulary incompatibility. In this work we introduce FastDraft, a novel and efficient approach for pre-training and aligning a draft model to any large language model by incorporating efficient pre-training, followed by fine-tuning over synthetic datasets generated by the target model. We demonstrate FastDraft by training two highly parameter efficient drafts for the popular Phi-3-mini and Llama-3.1-8B models. Using FastDraft, we were able to produce a draft with approximately 10 billion tokens on a single server with 8 Intel^circledR Gaudi^circledR 2 accelerators in under 24 hours. Our results show that the draft model achieves impressive results in key metrics of acceptance rate, block efficiency and up to 3x memory bound speed up when evaluated on code completion and up to 2x in summarization, text completion and instruction tasks. We validate our theoretical findings through benchmarking on the latest Intel^circledR Core^{tiny TM} Ultra, achieving a wall-clock time speedup of up to 2x, indicating a significant reduction in runtime. Due to its high quality, FastDraft unlocks large language models inference on AI-PC and other edge-devices.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

Generating time series data using Generative Adversarial Networks (GANs) presents several prevalent challenges, such as slow convergence, information loss in embedding spaces, instability, and performance variability depending on the series length. To tackle these obstacles, we introduce a robust framework aimed at addressing and mitigating these issues effectively. This advanced framework integrates the benefits of an Autoencoder-generated embedding space with the adversarial training dynamics of GANs. This framework benefits from a time series-based loss function and oversight from a supervisory network, both of which capture the stepwise conditional distributions of the data effectively. The generator functions within the latent space, while the discriminator offers essential feedback based on the feature space. Moreover, we introduce an early generation algorithm and an improved neural network architecture to enhance stability and ensure effective generalization across both short and long time series. Through joint training, our framework consistently outperforms existing benchmarks, generating high-quality time series data across a range of real and synthetic datasets with diverse characteristics.

Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a O(Nlog N) memory footprint for a length N sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.

Large language models (LLMs) have recently shown remarkable performance across a wide range of tasks. However, the substantial number of parameters in LLMs contributes to significant latency during model inference. This is particularly evident when utilizing autoregressive decoding methods, which generate one token in a single forward process, thereby not fully capitalizing on the parallel computing capabilities of GPUs. In this paper, we propose a novel parallel decoding approach, namely hidden transfer, which decodes multiple successive tokens simultaneously in a single forward pass. The idea is to transfer the intermediate hidden states of the previous context to the pseudo hidden states of the future tokens to be generated, and then the pseudo hidden states will pass the following transformer layers thereby assimilating more semantic information and achieving superior predictive accuracy of the future tokens. Besides, we use the novel tree attention mechanism to simultaneously generate and verify multiple candidates of output sequences, which ensure the lossless generation and further improves the generation efficiency of our method. Experiments demonstrate the effectiveness of our method. We conduct a lot of analytic experiments to prove our motivation. In terms of acceleration metrics, we outperform all the single-model acceleration techniques, including Medusa and Self-Speculative decoding.

Autoregressive models excel in modeling sequential dependencies by enforcing causal constraints, yet they struggle to capture complex bidirectional patterns due to their unidirectional nature. In contrast, mask-based models leverage bidirectional context, enabling richer dependency modeling. However, they often assume token independence during prediction, which undermines the modeling of sequential dependencies. Additionally, the corruption of sequences through masking or absorption can introduce unnatural distortions, complicating the learning process. To address these issues, we propose Bidirectional Autoregressive Diffusion (BAD), a novel approach that unifies the strengths of autoregressive and mask-based generative models. BAD utilizes a permutation-based corruption technique that preserves the natural sequence structure while enforcing causal dependencies through randomized ordering, enabling the effective capture of both sequential and bidirectional relationships. Comprehensive experiments show that BAD outperforms autoregressive and mask-based models in text-to-motion generation, suggesting a novel pre-training strategy for sequence modeling. The codebase for BAD is available on https://github.com/RohollahHS/BAD.

Autoregressive large language models (LLMs) have made remarkable progress in various natural language generation tasks. However, they incur high computation cost and latency resulting from the autoregressive token-by-token generation. To address this issue, several approaches have been proposed to reduce computational cost using early-exit strategies. These strategies enable faster text generation using reduced computation without applying the full computation graph to each token. While existing token-level early exit methods show promising results for online inference, they cannot be readily applied for batch inferencing and Key-Value caching. This is because they have to wait until the last token in a batch exits before they can stop computing. This severely limits the practical application of such techniques. In this paper, we propose a simple and effective token-level early exit method, SkipDecode, designed to work seamlessly with batch inferencing and KV caching. It overcomes prior constraints by setting up a singular exit point for every token in a batch at each sequence position. It also guarantees a monotonic decrease in exit points, thereby eliminating the need to recompute KV Caches for preceding tokens. Rather than terminating computation prematurely as in prior works, our approach bypasses lower to middle layers, devoting most of the computational resources to upper layers, allowing later tokens to benefit from the compute expenditure by earlier tokens. Our experimental results show that SkipDecode can obtain 2x to 5x inference speedups with negligible regression across a variety of tasks. This is achieved using OPT models of 1.3 billion and 6.7 billion parameters, all the while being directly compatible with batching and KV caching optimization techniques.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

Nowadays, with the rising number of sensors in sectors such as healthcare and industry, the problem of multivariate time series classification (MTSC) is getting increasingly relevant and is a prime target for machine and deep learning approaches. Their expanding adoption in real-world environments is causing a shift in focus from the pursuit of ever-higher prediction accuracy with complex models towards practical, deployable solutions that balance accuracy and parameters such as prediction speed. An MTSC model that has attracted attention recently is ROCKET, based on random convolutional kernels, both because of its very fast training process and its state-of-the-art accuracy. However, the large number of features it utilizes may be detrimental to inference time. Examining its theoretical background and limitations enables us to address potential drawbacks and present LightWaveS: a framework for accurate MTSC, which is fast both during training and inference. Specifically, utilizing wavelet scattering transformation and distributed feature selection, we manage to create a solution that employs just 2.5% of the ROCKET features, while achieving accuracy comparable to recent MTSC models. LightWaveS also scales well across multiple compute nodes and with the number of input channels during training. In addition, it can significantly reduce the input size and provide insight to an MTSC problem by keeping only the most useful channels. We present three versions of our algorithm and their results on distributed training time and scalability, accuracy, and inference speedup. We show that we achieve speedup ranging from 9x to 53x compared to ROCKET during inference on an edge device, on datasets with comparable accuracy.

Developing architectures suitable for modeling raw audio is a challenging problem due to the high sampling rates of audio waveforms. Standard sequence modeling approaches like RNNs and CNNs have previously been tailored to fit the demands of audio, but the resultant architectures make undesirable computational tradeoffs and struggle to model waveforms effectively. We propose SaShiMi, a new multi-scale architecture for waveform modeling built around the recently introduced S4 model for long sequence modeling. We identify that S4 can be unstable during autoregressive generation, and provide a simple improvement to its parameterization by drawing connections to Hurwitz matrices. SaShiMi yields state-of-the-art performance for unconditional waveform generation in the autoregressive setting. Additionally, SaShiMi improves non-autoregressive generation performance when used as the backbone architecture for a diffusion model. Compared to prior architectures in the autoregressive generation setting, SaShiMi generates piano and speech waveforms which humans find more musical and coherent respectively, e.g. 2x better mean opinion scores than WaveNet on an unconditional speech generation task. On a music generation task, SaShiMi outperforms WaveNet on density estimation and speed at both training and inference even when using 3x fewer parameters. Code can be found at https://github.com/HazyResearch/state-spaces and samples at https://hazyresearch.stanford.edu/sashimi-examples.

Auto-regressive decoding makes the inference of Large Language Models (LLMs) time-consuming. We propose a simple framework, EAGLE (Extrapolation Algorithm for Greater Language-model Efficiency), for lossless acceleration. Unlike traditional speculative sampling methods, EAGLE operates the drafting process auto-regressively at the more regular (second-top-layer) feature level and addresses the sampling uncertainty issues in the next-feature prediction problems by integrating tokens from one time step ahead. The acceleration provided by EAGLE is lossless: it involves no fine-tuning of the target LLM, and the generated text maintains the same distribution as that of vanilla auto-regressive decoding. As of the submission of this paper, EAGLE is the fastest known framework within the speculative sampling family. On MT-bench, EAGLE is 3x faster than vanilla decoding, 2x faster than Lookahead, and 1.6x faster than Medusa. Using gpt-fast, EAGLE attains on average 160 tokens/s with LLaMA2-Chat 13B on a single RTX 3090 GPU, compared to 24 tokens/s of Huggingface's implementations.

Large pre-trained models for zero/few-shot learning excel in language and vision domains but encounter challenges in multivariate time series (TS) due to the diverse nature and scarcity of publicly available pre-training data. Consequently, there has been a recent surge in utilizing pre-trained large language models (LLMs) with token adaptations for TS forecasting. These approaches employ cross-domain transfer learning and surprisingly yield impressive results. However, these models are typically very slow and large (~billion parameters) and do not consider cross-channel correlations. To address this, we present Tiny Time Mixers (TTM), a significantly small model based on the lightweight TSMixer architecture. TTM marks the first success in developing fast and tiny general pre-trained models (<1M parameters), exclusively trained on public TS datasets, with effective transfer learning capabilities for forecasting. To tackle the complexity of pre-training on multiple datasets with varied temporal resolutions, we introduce several novel enhancements such as adaptive patching, dataset augmentation via downsampling, and resolution prefix tuning. Moreover, we employ a multi-level modeling strategy to effectively model channel correlations and infuse exogenous signals during fine-tuning, a crucial capability lacking in existing benchmarks. TTM shows significant accuracy gains (12-38\%) over popular benchmarks in few/zero-shot forecasting. It also drastically reduces the compute needs as compared to LLM-TS methods, with a 14X cut in learnable parameters, 106X less total parameters, and substantial reductions in fine-tuning (65X) and inference time (54X). In fact, TTM's zero-shot often surpasses the few-shot results in many popular benchmarks, highlighting the efficacy of our approach. Code and pre-trained models will be open-sourced.

Next-Token Prediction (NTP) is a de facto approach for autoregressive (AR) video generation, but it suffers from suboptimal unidirectional dependencies and slow inference speed. In this work, we propose a semi-autoregressive (semi-AR) framework, called Next-Block Prediction (NBP), for video generation. By uniformly decomposing video content into equal-sized blocks (e.g., rows or frames), we shift the generation unit from individual tokens to blocks, allowing each token in the current block to simultaneously predict the corresponding token in the next block. Unlike traditional AR modeling, our framework employs bidirectional attention within each block, enabling tokens to capture more robust spatial dependencies. By predicting multiple tokens in parallel, NBP models significantly reduce the number of generation steps, leading to faster and more efficient inference. Our model achieves FVD scores of 103.3 on UCF101 and 25.5 on K600, outperforming the vanilla NTP model by an average of 4.4. Furthermore, thanks to the reduced number of inference steps, the NBP model generates 8.89 frames (128x128 resolution) per second, achieving an 11x speedup. We also explored model scales ranging from 700M to 3B parameters, observing significant improvements in generation quality, with FVD scores dropping from 103.3 to 55.3 on UCF101 and from 25.5 to 19.5 on K600, demonstrating the scalability of our approach.

Large Language Models (LLMs) frequently suffer from inefficiencies, largely attributable to the discord between the requirements of auto-regressive decoding and the architecture of contemporary GPUs. Recently, regressive lightweight speculative decoding has garnered attention for its notable efficiency improvements in text generation tasks. This approach utilizes a lightweight regressive draft model, like a Recurrent Neural Network (RNN) or a single transformer decoder layer, leveraging sequential information to iteratively predict potential tokens. Specifically, RNN draft models are computationally economical but tend to deliver lower accuracy, while attention decoder layer models exhibit the opposite traits. This paper presents Clover-2, an advanced iteration of Clover, an RNN-based draft model designed to achieve comparable accuracy to that of attention decoder layer models while maintaining minimal computational overhead. Clover-2 enhances the model architecture and incorporates knowledge distillation to increase Clover's accuracy and improve overall efficiency. We conducted experiments using the open-source Vicuna 7B and LLaMA3-Instruct 8B models. The results demonstrate that Clover-2 surpasses existing methods across various model architectures, showcasing its efficacy and robustness.

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, including quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a ProbSparse self-attention mechanism, which achieves O(L log L) in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

We introduce ARPG, a novel visual autoregressive model that enables randomized parallel generation, addressing the inherent limitations of conventional raster-order approaches, which hinder inference efficiency and zero-shot generalization due to their sequential, predefined token generation order. Our key insight is that effective random-order modeling necessitates explicit guidance for determining the position of the next predicted token. To this end, we propose a novel guided decoding framework that decouples positional guidance from content representation, encoding them separately as queries and key-value pairs. By directly incorporating this guidance into the causal attention mechanism, our approach enables fully random-order training and generation, eliminating the need for bidirectional attention. Consequently, ARPG readily generalizes to zero-shot tasks such as image inpainting, outpainting, and resolution expansion. Furthermore, it supports parallel inference by concurrently processing multiple queries using a shared KV cache. On the ImageNet-1K 256 benchmark, our approach attains an FID of 1.94 with only 64 sampling steps, achieving over a 20-fold increase in throughput while reducing memory consumption by over 75% compared to representative recent autoregressive models at a similar scale.

We present VARGPT, a novel multimodal large language model (MLLM) that unifies visual understanding and generation within a single autoregressive framework. VARGPT employs a next-token prediction paradigm for visual understanding and a next-scale prediction paradigm for visual autoregressive generation. VARGPT innovatively extends the LLaVA architecture, achieving efficient scale-wise autoregressive visual generation within MLLMs while seamlessly accommodating mixed-modal input and output within a single model framework. Our VARGPT undergoes a three-stage unified training process on specially curated datasets, comprising a pre-training phase and two mixed visual instruction-tuning phases. The unified training strategy are designed to achieve alignment between visual and textual features, enhance instruction following for both understanding and generation, and improve visual generation quality, respectively. Despite its LLAVA-based architecture for multimodel understanding, VARGPT significantly outperforms LLaVA-1.5 across various vision-centric benchmarks, such as visual question-answering and reasoning tasks. Notably, VARGPT naturally supports capabilities in autoregressive visual generation and instruction-to-image synthesis, showcasing its versatility in both visual understanding and generation tasks. Project page is at: https://vargpt-1.github.io/

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world small-sample scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progresses have been achieved as the emergence of large language models, exhibiting unprecedented ability in few-shot generalization, scalability, and task generality, which is however absent in time series models. To change the current practices of training small models on specific datasets from scratch, this paper aims at an early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), that is pre-trained by autoregressive next token prediction on large multi-domain datasets, and is fine-tuned to downstream scenarios with promising abilities as an LTSM.

In this report, we explore the potential for text diffusion to replace autoregressive (AR) decoding for the training and deployment of large language models (LLMs). We are particularly interested to see whether pretrained AR models can be transformed into text diffusion models through a lightweight adaptation procedure we call ``AR2Diff''. We begin by establishing a strong baseline setup for training text diffusion models. Comparing across multiple architectures and pretraining objectives, we find that training a decoder-only model with a prefix LM objective is best or near-best across several tasks. Building on this finding, we test various transfer learning setups for text diffusion models. On machine translation, we find that text diffusion underperforms the standard AR approach. However, on code synthesis and extractive QA, we find diffusion models trained from scratch outperform AR models in many cases. We also observe quality gains from AR2Diff -- adapting AR models to use diffusion decoding. These results are promising given that text diffusion is relatively underexplored and can be significantly faster than AR decoding for long text generation.

In this study, we propose Feature-aligned N-BEATS as a domain generalization model for univariate time series forecasting problems. The proposed model is an extension of the doubly residual stacking architecture of N-BEATS (Oreshkin et al. [34]) into a representation learning framework. The model is a new structure that involves marginal feature probability measures (i.e., pushforward measures of multiple source domains) induced by the intricate composition of residual operators of N-BEATS in each stack and aligns them stack-wise via an entropic regularized Wasserstein distance referred to as the Sinkhorn divergence (Genevay et al. [14]). The loss function consists of a typical forecasting loss for multiple source domains and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wise across multiple source data sequences while retaining N-BEATS's interpretable design. We conduct a comprehensive experimental evaluation of the proposed approach and the results demonstrate the model's forecasting and generalization capabilities in comparison with methods based on the original N-BEATS.

Autoregressive (AR) models have demonstrated impressive capabilities in generating high-fidelity music. However, the conventional next-token prediction paradigm in AR models does not align with the human creative process in music composition, potentially compromising the musicality of generated samples. To overcome this limitation, we introduce MusiCoT, a novel chain-of-thought (CoT) prompting technique tailored for music generation. MusiCoT empowers the AR model to first outline an overall music structure before generating audio tokens, thereby enhancing the coherence and creativity of the resulting compositions. By leveraging the contrastive language-audio pretraining (CLAP) model, we establish a chain of "musical thoughts", making MusiCoT scalable and independent of human-labeled data, in contrast to conventional CoT methods. Moreover, MusiCoT allows for in-depth analysis of music structure, such as instrumental arrangements, and supports music referencing -- accepting variable-length audio inputs as optional style references. This innovative approach effectively addresses copying issues, positioning MusiCoT as a vital practical method for music prompting. Our experimental results indicate that MusiCoT consistently achieves superior performance across both objective and subjective metrics, producing music quality that rivals state-of-the-art generation models. Our samples are available at https://MusiCoT.github.io/.

Recent advances in autoregressive (AR) models with continuous tokens for image generation show promising results by eliminating the need for discrete tokenization. However, these models face efficiency challenges due to their sequential token generation nature and reliance on computationally intensive diffusion-based sampling. We present ECAR (Efficient Continuous Auto-Regressive Image Generation via Multistage Modeling), an approach that addresses these limitations through two intertwined innovations: (1) a stage-wise continuous token generation strategy that reduces computational complexity and provides progressively refined token maps as hierarchical conditions, and (2) a multistage flow-based distribution modeling method that transforms only partial-denoised distributions at each stage comparing to complete denoising in normal diffusion models. Holistically, ECAR operates by generating tokens at increasing resolutions while simultaneously denoising the image at each stage. This design not only reduces token-to-image transformation cost by a factor of the stage number but also enables parallel processing at the token level. Our approach not only enhances computational efficiency but also aligns naturally with image generation principles by operating in continuous token space and following a hierarchical generation process from coarse to fine details. Experimental results demonstrate that ECAR achieves comparable image quality to DiT Peebles & Xie [2023] while requiring 10times FLOPs reduction and 5times speedup to generate a 256times256 image.

Many applications today provide users with multiple auto-complete drafts as they type, including GitHub's code completion, Gmail's smart compose, and Apple's messaging auto-suggestions. Under the hood, language models support this by running an autoregressive inference pass to provide a draft. Consequently, providing k drafts to the user requires running an expensive language model k times. To alleviate the computation cost of running k inference passes, we propose Superposed Decoding, a new decoding algorithm that generates k drafts at the computation cost of one autoregressive inference pass. We achieve this by feeding a superposition of the most recent token embeddings from the k drafts as input to the next decoding step of the language model. At every inference step we combine the k drafts with the top-k tokens to get k^2 new drafts and cache the k most likely options, using an n-gram interpolation with minimal compute overhead to filter out incoherent generations. Our experiments show that k drafts from Superposed Decoding are at least as coherent and factual as Nucleus Sampling and Greedy Decoding respectively, while being at least 2.44times faster for kge3. In a compute-normalized setting, user evaluations demonstrably favor text generated by Superposed Decoding over Nucleus Sampling. Code and more examples open-sourced at https://github.com/RAIVNLab/SuperposedDecoding.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

Predicting the bandwidth utilization on network links can be extremely useful for detecting congestion in order to correct them before they occur. In this paper, we present a solution to predict the bandwidth utilization between different network links with a very high accuracy. A simulated network is created to collect data related to the performance of the network links on every interface. These data are processed and expanded with feature engineering in order to create a training set. We evaluate and compare three types of machine learning algorithms, namely ARIMA (AutoRegressive Integrated Moving Average), MLP (Multi Layer Perceptron) and LSTM (Long Short-Term Memory), in order to predict the future bandwidth consumption. The LSTM outperforms ARIMA and MLP with very accurate predictions, rarely exceeding a 3\% error (40\% for ARIMA and 20\% for the MLP). We then show that the proposed solution can be used in real time with a reaction managed by a Software-Defined Networking (SDN) platform.

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

We introduce Reward-Guided Speculative Decoding (RSD), a novel framework aimed at improving the efficiency of inference in large language models (LLMs). RSD synergistically combines a lightweight draft model with a more powerful target model, incorporating a controlled bias to prioritize high-reward outputs, in contrast to existing speculative decoding methods that enforce strict unbiasedness. RSD employs a process reward model to evaluate intermediate decoding steps and dynamically decide whether to invoke the target model, optimizing the trade-off between computational cost and output quality. We theoretically demonstrate that a threshold-based mixture strategy achieves an optimal balance between resource utilization and performance. Extensive evaluations on challenging reasoning benchmarks, including Olympiad-level tasks, show that RSD delivers significant efficiency gains against decoding with the target model only (up to 4.4x fewer FLOPs), while achieving significant better accuracy than parallel decoding method on average (up to +3.5). These results highlight RSD as a robust and cost-effective approach for deploying LLMs in resource-intensive scenarios.

Time series foundation models excel in zero-shot forecasting, handling diverse tasks without explicit training. However, the advancement of these models has been hindered by the lack of comprehensive benchmarks. To address this gap, we introduce the General Time Series Forecasting Model Evaluation, GIFT-Eval, a pioneering benchmark aimed at promoting evaluation across diverse datasets. GIFT-Eval encompasses 28 datasets over 144,000 time series and 177 million data points, spanning seven domains, 10 frequencies, multivariate inputs, and prediction lengths ranging from short to long-term forecasts. To facilitate the effective pretraining and evaluation of foundation models, we also provide a non-leaking pretraining dataset containing approximately 230 billion data points. Additionally, we provide a comprehensive analysis of 17 baselines, which includes statistical models, deep learning models, and foundation models. We discuss each model in the context of various benchmark characteristics and offer a qualitative analysis that spans both deep learning and foundation models. We believe the insights from this analysis, along with access to this new standard zero-shot time series forecasting benchmark, will guide future developments in time series foundation models. The codebase, datasets, and a leaderboard showing all the results in detail will be available soon.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Speculative decoding enhances the efficiency of large language models (LLMs) by leveraging a draft model to draft for a larger target model to review. However, drafting in speculative decoding involves slow autoregressive generation and generating tokens of different importance with the same time allocation. These two inefficiencies lead to its suboptimal performance. To address this issue, we introduce Cascade Speculative Drafting (CS. Drafting), a novel approach that employs two types of cascades. The Vertical Cascade eliminates autoregressive generation from neural models. The Horizontal Cascade constitutes efficient time allocation in drafting with its optimality supported by our theoretical analysis. Combining both cascades, our CS. Drafting algorithm has achieved up to 72 percent additional speedup over speculative decoding in our experiments while keeping the same output distribution.

Diffusion language models offer unique benefits over autoregressive models due to their potential for parallelized generation and controllability, yet they lag in likelihood modeling and are limited to fixed-length generation. In this work, we introduce a class of block diffusion language models that interpolate between discrete denoising diffusion and autoregressive models. Block diffusion overcomes key limitations of both approaches by supporting flexible-length generation and improving inference efficiency with KV caching and parallel token sampling. We propose a recipe for building effective block diffusion models that includes an efficient training algorithm, estimators of gradient variance, and data-driven noise schedules to minimize the variance. Block diffusion sets a new state-of-the-art performance among diffusion models on language modeling benchmarks and enables generation of arbitrary-length sequences. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/bd3lms/

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

Striking an optimal balance between minimal drafting latency and high speculation accuracy to enhance the inference speed of Large Language Models remains a significant challenge in speculative decoding. In this paper, we introduce Falcon, an innovative semi-autoregressive speculative decoding framework fashioned to augment both the drafter's parallelism and output quality. Falcon incorporates the Coupled Sequential Glancing Distillation technique, which fortifies inter-token dependencies within the same block, leading to increased speculation accuracy. We offer a comprehensive theoretical analysis to illuminate the underlying mechanisms. Additionally, we introduce a Custom-Designed Decoding Tree, which permits the drafter to generate multiple tokens in a single forward pass and accommodates multiple forward passes as needed, thereby boosting the number of drafted tokens and significantly improving the overall acceptance rate. Comprehensive evaluations on benchmark datasets such as MT-Bench, HumanEval, and GSM8K demonstrate Falcon's superior acceleration capabilities. The framework achieves a lossless speedup ratio ranging from 2.91x to 3.51x when tested on the Vicuna and LLaMA2-Chat model series. These results outstrip existing speculative decoding methods for LLMs, including Eagle, Medusa, Lookahead, SPS, and PLD, while maintaining a compact drafter architecture equivalent to merely two Transformer layers.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

Code generation is a latency-sensitive task that demands high timeliness, but the autoregressive decoding mechanism of Large Language Models (LLMs) leads to poor inference efficiency. Existing LLM inference acceleration methods mainly focus on standalone functions using only built-in components. Moreover, they treat code like natural language sequences, ignoring its unique syntax and semantic characteristics. As a result, the effectiveness of these approaches in code generation tasks remains limited and fails to align with real-world programming scenarios. To alleviate this issue, we propose CodeSwift, a simple yet highly efficient inference acceleration approach specifically designed for code generation, without comprising the quality of the output. CodeSwift constructs a multi-source datastore, providing access to both general and project-specific knowledge, facilitating the retrieval of high-quality draft sequences. Moreover, CodeSwift reduces retrieval cost by controlling retrieval timing, and enhances efficiency through parallel retrieval and a context- and LLM preference-aware cache. Experimental results show that CodeSwift can reach up to 2.53x and 2.54x speedup compared to autoregressive decoding in repository-level and standalone code generation tasks, respectively, outperforming state-of-the-art inference acceleration approaches by up to 88%.

Parameter-shared pre-trained language models (PLMs) have emerged as a successful approach in resource-constrained environments, enabling substantial reductions in model storage and memory costs without significant performance compromise. However, it is important to note that parameter sharing does not alleviate computational burdens associated with inference, thus impeding its practicality in situations characterized by limited stringent latency requirements or computational resources. Building upon neural ordinary differential equations (ODEs), we introduce a straightforward technique to enhance the inference efficiency of parameter-shared PLMs. Additionally, we propose a simple pre-training technique that leads to fully or partially shared models capable of achieving even greater inference acceleration. The experimental results demonstrate the effectiveness of our methods on both autoregressive and autoencoding PLMs, providing novel insights into more efficient utilization of parameter-shared models in resource-constrained settings.

Drafting-then-verifying decoding methods such as speculative decoding are widely adopted training-free methods to accelerate the inference of large language models (LLMs). Instead of employing an autoregressive process to decode tokens sequentially, speculative decoding initially creates drafts with an efficient small model. Then LLMs are required to conduct verification and correction in a non-autoregressive fashion to minimize time overhead. Generating longer drafts can lead to even more significant speedups once verified, but also incurs substantial trial and error costs if it fails. Suffering from the high verification failure probability, existing decoding methods cannot draft too much content for verification at one time, achieving sub-optimal inference acceleration. In this paper, we introduce Ouroboros, which constructs a phrase candidate pool from the verification process of LLMs to provide candidates for draft generation of the small model. Thereby, Ouroboros can further improve the efficiency and effectiveness of the initial drafts. The experimental results on typical text generation tasks show that Ouroboros achieves speedups of up to 1.9x and 2.8x compared to lookahead decoding and speculative decoding, respectively. The source code of Ouroboros is available at https://github.com/thunlp/Ouroboros.

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

Autoregressive decoding of large language models (LLMs) is memory bandwidth bounded, resulting in high latency and significant wastes of the parallel processing power of modern accelerators. Existing methods for accelerating LLM decoding often require a draft model (e.g., speculative decoding), which is nontrivial to obtain and unable to generalize. In this paper, we introduce Lookahead decoding, an exact, parallel decoding algorithm that accelerates LLM decoding without needing auxiliary models or data stores. It allows trading per-step log(FLOPs) to reduce the number of total decoding steps, is more parallelizable on single or multiple modern accelerators, and is compatible with concurrent memory-efficient attention (e.g., FlashAttention). Our implementation of Lookahead decoding can speed up autoregressive decoding by up to 1.8x on MT-bench and 4x with strong scaling on multiple GPUs in code completion tasks. Our code is avialable at https://github.com/hao-ai-lab/LookaheadDecoding

Diffusion language models have emerged as a promising approach for text generation. One would naturally expect this method to be an efficient replacement for autoregressive models since multiple tokens can be sampled in parallel during each diffusion step. However, its efficiency-accuracy trade-off is not yet well understood. In this paper, we present a rigorous theoretical analysis of a widely used type of diffusion language model, the Masked Diffusion Model (MDM), and find that its effectiveness heavily depends on the target evaluation metric. Under mild conditions, we prove that when using perplexity as the metric, MDMs can achieve near-optimal perplexity in sampling steps regardless of sequence length, demonstrating that efficiency can be achieved without sacrificing performance. However, when using the sequence error rate--which is important for understanding the "correctness" of a sequence, such as a reasoning chain--we show that the required sampling steps must scale linearly with sequence length to obtain "correct" sequences, thereby eliminating MDM's efficiency advantage over autoregressive models. Our analysis establishes the first theoretical foundation for understanding the benefits and limitations of MDMs. All theoretical findings are supported by empirical studies.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.