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Jul 10

GWQ: Gradient-Aware Weight Quantization for Large Language Models

Large language models (LLMs) show impressive performance in solving complex language tasks. However, its large number of parameters present significant challenges for the deployment and application of the model on edge devices. Compressing large language models to low bits can enable them to run on resource-constrained devices, often leading to performance degradation. To address this problem, we propose gradient-aware weight quantization (GWQ), the first quantization approach for low-bit weight quantization that leverages gradients to localize outliers, requiring only a minimal amount of calibration data for outlier detection. GWQ retains the weights corresponding to the top 1% outliers preferentially at FP16 precision, while the remaining non-outlier weights are stored in a low-bit format. GWQ found experimentally that utilizing the sensitive weights in the gradient localization model is more scientific compared to utilizing the sensitive weights in the Hessian matrix localization model. Compared to current quantization methods, GWQ can be applied to multiple language models and achieves lower PPL on the WikiText2 and C4 dataset. In the zero-shot task, GWQ quantized models have higher accuracy compared to other quantization methods. GWQ is also suitable for multimodal model quantization, and the quantized Qwen-VL family model is more accurate than other methods. Zero-shot target detection task dataset RefCOCO outperforms the current stat-of-the-arts method SPQR. GWQ achieves 1.2 times inference speedup in comparison to the original model, and effectively reduces the inference memory.

AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration

Large language models (LLMs) have shown excellent performance on various tasks, but the astronomical model size raises the hardware barrier for serving (memory size) and slows down token generation (memory bandwidth). In this paper, we propose Activation-aware Weight Quantization (AWQ), a hardware-friendly approach for LLM low-bit weight-only quantization. Our method is based on the observation that weights are not equally important: protecting only 1% of salient weights can greatly reduce quantization error. We then propose to search for the optimal per-channel scaling that protects the salient weights by observing the activation, not weights. AWQ does not rely on any backpropagation or reconstruction, so it can well preserve LLMs' generalization ability on different domains and modalities, without overfitting to the calibration set; it also does not rely on any data layout reordering, maintaining the hardware efficiency. AWQ outperforms existing work on various language modeling, common sense QA, and domain-specific benchmarks. Thanks to better generalization, it achieves excellent quantization performance for instruction-tuned LMs and, for the first time, multi-modal LMs. We also implement efficient tensor core kernels with reorder-free online dequantization to accelerate AWQ, achieving a 1.45x speedup over GPTQ and is 1.85x faster than the cuBLAS FP16 implementation. Our method provides a turn-key solution to compress LLMs to 3/4 bits for efficient deployment.

Gradient-Based Post-Training Quantization: Challenging the Status Quo

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

Oscillation-free Quantization for Low-bit Vision Transformers

Weight oscillation is an undesirable side effect of quantization-aware training, in which quantized weights frequently jump between two quantized levels, resulting in training instability and a sub-optimal final model. We discover that the learnable scaling factor, a widely-used de facto setting in quantization aggravates weight oscillation. In this study, we investigate the connection between the learnable scaling factor and quantized weight oscillation and use ViT as a case driver to illustrate the findings and remedies. In addition, we also found that the interdependence between quantized weights in query and key of a self-attention layer makes ViT vulnerable to oscillation. We, therefore, propose three techniques accordingly: statistical weight quantization (rm StatsQ) to improve quantization robustness compared to the prevalent learnable-scale-based method; confidence-guided annealing (rm CGA) that freezes the weights with high confidence and calms the oscillating weights; and query-key reparameterization (rm QKR) to resolve the query-key intertwined oscillation and mitigate the resulting gradient misestimation. Extensive experiments demonstrate that these proposed techniques successfully abate weight oscillation and consistently achieve substantial accuracy improvement on ImageNet. Specifically, our 2-bit DeiT-T/DeiT-S algorithms outperform the previous state-of-the-art by 9.8% and 7.7%, respectively. Code and models are available at: https://github.com/nbasyl/OFQ.

GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers

Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically, due to their massive size, even inference for large, highly-accurate GPT models may require multiple performant GPUs, which limits the usability of such models. While there is emerging work on relieving this pressure via model compression, the applicability and performance of existing compression techniques is limited by the scale and complexity of GPT models. In this paper, we address this challenge, and propose GPTQ, a new one-shot weight quantization method based on approximate second-order information, that is both highly-accurate and highly-efficient. Specifically, GPTQ can quantize GPT models with 175 billion parameters in approximately four GPU hours, reducing the bitwidth down to 3 or 4 bits per weight, with negligible accuracy degradation relative to the uncompressed baseline. Our method more than doubles the compression gains relative to previously-proposed one-shot quantization methods, preserving accuracy, allowing us for the first time to execute an 175 billion-parameter model inside a single GPU for generative inference. Moreover, we also show that our method can still provide reasonable accuracy in the extreme quantization regime, in which weights are quantized to 2-bit or even ternary quantization levels. We show experimentally that these improvements can be leveraged for end-to-end inference speedups over FP16, of around 3.25x when using high-end GPUs (NVIDIA A100) and 4.5x when using more cost-effective ones (NVIDIA A6000). The implementation is available at https://github.com/IST-DASLab/gptq.

GQSA: Group Quantization and Sparsity for Accelerating Large Language Model Inference

Model compression has emerged as a mainstream solution to reduce memory usage and computational overhead. This paper presents Group Quantization and Sparse Acceleration (GQSA), a novel compression technique tailored for LLMs. Traditional methods typically focus exclusively on either quantization or sparsification, but relying on a single strategy often results in significant performance loss at high compression rates. In contrast, GQSA integrates quantization and sparsification in a tightly coupled manner, leveraging GPU-friendly structured group sparsity and quantization for efficient acceleration. Building upon system-algorithm co-design principles, we propose a two-stage sparse optimization strategy that ensures the performance superiority of the compressed model. On the engine side, we introduce a "task-centric" parallel strategy, which, to the best of our knowledge, is the first application in the domain of sparse computing. Compared to the traditional 2:4 sparse method, the GQSA offers a more flexible and adjustable sparsity rate, as well as a higher weight compression rate, and is efficiently compatible with weight-only quantization methods. Experimental results demonstrate that, under the GQSA W4S50% compression setting, the model's accuracy surpasses that of both 2:4 pruning and W2 quantization. Furthermore, at the inference level, GQSA outperforms W2 by 1.26times and 2:4 pruning by 2.35times in terms of speed.

GAQAT: gradient-adaptive quantization-aware training for domain generalization

Research on loss surface geometry, such as Sharpness-Aware Minimization (SAM), shows that flatter minima improve generalization. Recent studies further reveal that flatter minima can also reduce the domain generalization (DG) gap. However, existing flatness-based DG techniques predominantly operate within a full-precision training process, which is impractical for deployment on resource-constrained edge devices that typically rely on lower bit-width representations (e.g., 4 bits, 3 bits). Consequently, low-precision quantization-aware training is critical for optimizing these techniques in real-world applications. In this paper, we observe a significant degradation in performance when applying state-of-the-art DG-SAM methods to quantized models, suggesting that current approaches fail to preserve generalizability during the low-precision training process. To address this limitation, we propose a novel Gradient-Adaptive Quantization-Aware Training (GAQAT) framework for DG. Our approach begins by identifying the scale-gradient conflict problem in low-precision quantization, where the task loss and smoothness loss induce conflicting gradients for the scaling factors of quantizers, with certain layers exhibiting opposing gradient directions. This conflict renders the optimization of quantized weights highly unstable. To mitigate this, we further introduce a mechanism to quantify gradient inconsistencies and selectively freeze the gradients of scaling factors, thereby stabilizing the training process and enhancing out-of-domain generalization. Extensive experiments validate the effectiveness of the proposed GAQAT framework. On PACS, our 3-bit and 4-bit models outperform direct DG-QAT integration by up to 4.5%. On DomainNet, the 4-bit model achieves near-lossless performance compared to full precision, with improvements of 1.39% (4-bit) and 1.06% (3-bit) over the SOTA QAT baseline.

DGQ: Distribution-Aware Group Quantization for Text-to-Image Diffusion Models

Despite the widespread use of text-to-image diffusion models across various tasks, their computational and memory demands limit practical applications. To mitigate this issue, quantization of diffusion models has been explored. It reduces memory usage and computational costs by compressing weights and activations into lower-bit formats. However, existing methods often struggle to preserve both image quality and text-image alignment, particularly in lower-bit(< 8bits) quantization. In this paper, we analyze the challenges associated with quantizing text-to-image diffusion models from a distributional perspective. Our analysis reveals that activation outliers play a crucial role in determining image quality. Additionally, we identify distinctive patterns in cross-attention scores, which significantly affects text-image alignment. To address these challenges, we propose Distribution-aware Group Quantization (DGQ), a method that identifies and adaptively handles pixel-wise and channel-wise outliers to preserve image quality. Furthermore, DGQ applies prompt-specific logarithmic quantization scales to maintain text-image alignment. Our method demonstrates remarkable performance on datasets such as MS-COCO and PartiPrompts. We are the first to successfully achieve low-bit quantization of text-to-image diffusion models without requiring additional fine-tuning of weight quantization parameters. Code is available at https://github.com/ugonfor/DGQ.

RSQ: Learning from Important Tokens Leads to Better Quantized LLMs

Layer-wise quantization is a key technique for efficiently compressing large models without expensive retraining. Previous methods typically quantize the weights of each layer by "uniformly" optimizing the layer reconstruction loss across all output tokens. However, in this paper, we demonstrate that better-quantized models can be obtained by prioritizing learning from important tokens (e.g. which have large attention scores). Building on this finding, we propose RSQ (Rotate, Scale, then Quantize), which (1) applies rotations (orthogonal transformation) to the model to mitigate outliers (those with exceptionally large magnitude), (2) scales the token feature based on its importance, and (3) quantizes the model using the GPTQ framework with the second-order statistics computed by scaled tokens. To compute token importance, we explore both heuristic and dynamic strategies. Based on a thorough analysis of all approaches, we adopt attention concentration, which uses attention scores of each token as its importance, as the best approach. We demonstrate that RSQ consistently outperforms baseline methods across multiple downstream tasks and three model families: LLaMA3, Mistral, and Qwen2.5. Additionally, models quantized with RSQ achieve superior performance on long-context tasks, further highlighting its effectiveness. Lastly, RSQ demonstrates generalizability across various setups, including different model sizes, calibration datasets, bit precisions, and quantization methods.

QServe: W4A8KV4 Quantization and System Co-design for Efficient LLM Serving

Quantization can accelerate large language model (LLM) inference. Going beyond INT8 quantization, the research community is actively exploring even lower precision, such as INT4. Nonetheless, state-of-the-art INT4 quantization techniques only accelerate low-batch, edge LLM inference, failing to deliver performance gains in large-batch, cloud-based LLM serving. We uncover a critical issue: existing INT4 quantization methods suffer from significant runtime overhead (20-90%) when dequantizing either weights or partial sums on GPUs. To address this challenge, we introduce QoQ, a W4A8KV4 quantization algorithm with 4-bit weight, 8-bit activation, and 4-bit KV cache. QoQ stands for quattuor-octo-quattuor, which represents 4-8-4 in Latin. QoQ is implemented by the QServe inference library that achieves measured speedup. The key insight driving QServe is that the efficiency of LLM serving on GPUs is critically influenced by operations on low-throughput CUDA cores. Building upon this insight, in QoQ algorithm, we introduce progressive quantization that can allow low dequantization overhead in W4A8 GEMM. Additionally, we develop SmoothAttention to effectively mitigate the accuracy degradation incurred by 4-bit KV quantization. In the QServe system, we perform compute-aware weight reordering and take advantage of register-level parallelism to reduce dequantization latency. We also make fused attention memory-bound, harnessing the performance gain brought by KV4 quantization. As a result, QServe improves the maximum achievable serving throughput of Llama-3-8B by 1.2x on A100, 1.4x on L40S; and Qwen1.5-72B by 2.4x on A100, 3.5x on L40S, compared to TensorRT-LLM. Remarkably, QServe on L40S GPU can achieve even higher throughput than TensorRT-LLM on A100. Thus, QServe effectively reduces the dollar cost of LLM serving by 3x. Code is available at https://github.com/mit-han-lab/qserve.

HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision

Model size and inference speed/power have become a major challenge in the deployment of Neural Networks for many applications. A promising approach to address these problems is quantization. However, uniformly quantizing a model to ultra low precision leads to significant accuracy degradation. A novel solution for this is to use mixed-precision quantization, as some parts of the network may allow lower precision as compared to other layers. However, there is no systematic way to determine the precision of different layers. A brute force approach is not feasible for deep networks, as the search space for mixed-precision is exponential in the number of layers. Another challenge is a similar factorial complexity for determining block-wise fine-tuning order when quantizing the model to a target precision. Here, we introduce Hessian AWare Quantization (HAWQ), a novel second-order quantization method to address these problems. HAWQ allows for the automatic selection of the relative quantization precision of each layer, based on the layer's Hessian spectrum. Moreover, HAWQ provides a deterministic fine-tuning order for quantizing layers, based on second-order information. We show the results of our method on Cifar-10 using ResNet20, and on ImageNet using Inception-V3, ResNet50 and SqueezeNext models. Comparing HAWQ with state-of-the-art shows that we can achieve similar/better accuracy with 8times activation compression ratio on ResNet20, as compared to DNAS~wu2018mixed, and up to 1% higher accuracy with up to 14% smaller models on ResNet50 and Inception-V3, compared to recently proposed methods of RVQuant~park2018value and HAQ~wang2018haq. Furthermore, we show that we can quantize SqueezeNext to just 1MB model size while achieving above 68% top1 accuracy on ImageNet.

VQ4DiT: Efficient Post-Training Vector Quantization for Diffusion Transformers

The Diffusion Transformers Models (DiTs) have transitioned the network architecture from traditional UNets to transformers, demonstrating exceptional capabilities in image generation. Although DiTs have been widely applied to high-definition video generation tasks, their large parameter size hinders inference on edge devices. Vector quantization (VQ) can decompose model weight into a codebook and assignments, allowing extreme weight quantization and significantly reducing memory usage. In this paper, we propose VQ4DiT, a fast post-training vector quantization method for DiTs. We found that traditional VQ methods calibrate only the codebook without calibrating the assignments. This leads to weight sub-vectors being incorrectly assigned to the same assignment, providing inconsistent gradients to the codebook and resulting in a suboptimal result. To address this challenge, VQ4DiT calculates the candidate assignment set for each weight sub-vector based on Euclidean distance and reconstructs the sub-vector based on the weighted average. Then, using the zero-data and block-wise calibration method, the optimal assignment from the set is efficiently selected while calibrating the codebook. VQ4DiT quantizes a DiT XL/2 model on a single NVIDIA A100 GPU within 20 minutes to 5 hours depending on the different quantization settings. Experiments show that VQ4DiT establishes a new state-of-the-art in model size and performance trade-offs, quantizing weights to 2-bit precision while retaining acceptable image generation quality.

QVGen: Pushing the Limit of Quantized Video Generative Models

Video diffusion models (DMs) have enabled high-quality video synthesis. Yet, their substantial computational and memory demands pose serious challenges to real-world deployment, even on high-end GPUs. As a commonly adopted solution, quantization has proven notable success in reducing cost for image DMs, while its direct application to video DMs remains ineffective. In this paper, we present QVGen, a novel quantization-aware training (QAT) framework tailored for high-performance and inference-efficient video DMs under extremely low-bit quantization (e.g., 4-bit or below). We begin with a theoretical analysis demonstrating that reducing the gradient norm is essential to facilitate convergence for QAT. To this end, we introduce auxiliary modules (Phi) to mitigate large quantization errors, leading to significantly enhanced convergence. To eliminate the inference overhead of Phi, we propose a rank-decay strategy that progressively eliminates Phi. Specifically, we repeatedly employ singular value decomposition (SVD) and a proposed rank-based regularization gamma to identify and decay low-contributing components. This strategy retains performance while zeroing out inference overhead. Extensive experiments across 4 state-of-the-art (SOTA) video DMs, with parameter sizes ranging from 1.3B sim14B, show that QVGen is the first to reach full-precision comparable quality under 4-bit settings. Moreover, it significantly outperforms existing methods. For instance, our 3-bit CogVideoX-2B achieves improvements of +25.28 in Dynamic Degree and +8.43 in Scene Consistency on VBench.

Enabling Fast 2-bit LLM on GPUs: Memory Alignment and Asynchronous Dequantization

Large language models (LLMs) have demonstrated impressive abilities in various domains while the inference cost is expensive. The state-of-the-art methods use 2-bit quantization for mainstream LLMs. However, challenges still exist: (1) Nonnegligible accuracy loss for 2-bit quantization. Weights are quantized by groups, while the ranges of weights are large in some groups, resulting in large quantization errors and nonnegligible accuracy loss (e.g. >3% for Llama2-7b with 2-bit quantization in GPTQ and Greenbit). (2) Limited accuracy improvement by adding 4-bit weights. Increasing 10% extra average bit more 4-bit weights only leads to <0.5% accuracy improvement on a quantized Llama2-7b. (3) Time-consuming dequantization operations on GPUs. The dequantization operations lead to >50% execution time, hindering the potential of reducing LLM inference cost. To tackle these challenges, we propose the following techniques: (1) We only quantize a small fraction of groups with the larger range using 4-bit with memory alignment consideration on GPUs.(2) We design the asynchronous dequantization on GPUs, leading to up to 3.92X speedup. We conduct extensive experiments on different model sizes. We achieve 2.85-bit for each weight and the end-to-end speedup for Llama2-7b is 1.74X over the original model, and we reduce both runtime cost and hardware cost by up to 2.70X and 2.81X with less GPU requirements.

EQ-Net: Elastic Quantization Neural Networks

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Fine-tuning Quantized Neural Networks with Zeroth-order Optimization

As the size of large language models grows exponentially, GPU memory has become a bottleneck for adapting these models to downstream tasks. In this paper, we aim to push the limits of memory-efficient training by minimizing memory usage on model weights, gradients, and optimizer states, within a unified framework. Our idea is to eliminate both gradients and optimizer states using zeroth-order optimization, which approximates gradients by perturbing weights during forward passes to identify gradient directions. To minimize memory usage on weights, we employ model quantization, e.g., converting from bfloat16 to int4. However, directly applying zeroth-order optimization to quantized weights is infeasible due to the precision gap between discrete weights and continuous gradients, which would otherwise require de-quantization and re-quantization. To overcome this challenge, we propose Quantized Zeroth-order Optimization (QZO), a novel approach that perturbs the continuous quantization scale for gradient estimation and uses a directional derivative clipping method to stabilize training. QZO is orthogonal to both scalar-based and codebook-based post-training quantization methods. Compared to full-parameter fine-tuning in bfloat16, QZO can reduce the total memory cost by more than 18times for 4-bit LLMs, and enables fine-tuning Llama-2-13B and Stable Diffusion 3.5 Large within a single 24GB GPU.

QuantEase: Optimization-based Quantization for Language Models

With the rising popularity of Large Language Models (LLMs), there has been an increasing interest in compression techniques that enable their efficient deployment. This study focuses on the Post-Training Quantization (PTQ) of LLMs. Drawing from recent advances, our work introduces QuantEase, a layer-wise quantization framework where individual layers undergo separate quantization. The problem is framed as a discrete-structured non-convex optimization, prompting the development of algorithms rooted in Coordinate Descent (CD) techniques. These CD-based methods provide high-quality solutions to the complex non-convex layer-wise quantization problems. Notably, our CD-based approach features straightforward updates, relying solely on matrix and vector operations, circumventing the need for matrix inversion or decomposition. We also explore an outlier-aware variant of our approach, allowing for retaining significant weights (outliers) with complete precision. Our proposal attains state-of-the-art performance in terms of perplexity and zero-shot accuracy in empirical evaluations across various LLMs and datasets, with relative improvements up to 15% over methods such as GPTQ. Leveraging careful linear algebra optimizations, QuantEase can quantize models like Falcon-180B on a single NVIDIA A100 GPU in sim3 hours. Particularly noteworthy is our outlier-aware algorithm's capability to achieve near or sub-3-bit quantization of LLMs with an acceptable drop in accuracy, obviating the need for non-uniform quantization or grouping techniques, improving upon methods such as SpQR by up to two times in terms of perplexity.

SmoothQuant+: Accurate and Efficient 4-bit Post-Training WeightQuantization for LLM

Large language models (LLMs) have shown remarkable capabilities in various tasks. However their huge model size and the consequent demand for computational and memory resources also pose challenges to model deployment. Currently, 4-bit post-training quantization (PTQ) has achieved some success in LLMs, reducing the memory footprint by approximately 75% compared to FP16 models, albeit with some accuracy loss. In this paper, we propose SmoothQuant+, an accurate and efficient 4-bit weight-only PTQ that requires no additional training, which enables lossless in accuracy for LLMs for the first time. Based on the fact that the loss of weight quantization is amplified by the activation outliers, SmoothQuant+ smoothes the activation outliers by channel before quantization, while adjusting the corresponding weights for mathematical equivalence, and then performs group-wise 4-bit weight quantization for linear layers. We have integrated SmoothQuant+ into the vLLM framework, an advanced high-throughput inference engine specially developed for LLMs, and equipped it with an efficient W4A16 CUDA kernels, so that vLLM can seamlessly support SmoothQuant+ 4-bit weight quantization. Our results show that, with SmoothQuant+, the Code Llama-34B model can be quantized and deployed on a A100 40GB GPU, achieving lossless accuracy and a throughput increase of 1.9 to 4.0 times compared to the FP16 model deployed on two A100 40GB GPUs. Moreover, the latency per token is only 68% of the FP16 model deployed on two A100 40GB GPUs. This is the state-of-the-art 4-bit weight quantization for LLMs as we know.

L4Q: Parameter Efficient Quantization-Aware Training on Large Language Models via LoRA-wise LSQ

Post-training quantization (PTQ) and quantization-aware training (QAT) methods are gaining popularity in mitigating the high memory and computational costs associated with Large Language Models (LLMs). In resource-constrained scenarios, PTQ, with its reduced training overhead, is often preferred over QAT, despite the latter's potential for higher accuracy. Meanwhile, parameter-efficient fine-tuning (PEFT) methods like low-rank adaptation (LoRA) have been introduced, and recent efforts have explored quantization-aware PEFT techniques. However, these approaches may lack generality due to their reliance on the pre-quantized model's configuration. Their effectiveness may be compromised by non-linearly quantized or mixed-precision weights, and the retraining of specific quantization parameters might impede optimal performance. To address these challenges, we propose L4Q, an algorithm for parameter-efficient quantization-aware training. L4Q leverages LoRA-wise learned quantization step size for LLMs, aiming to enhance generality. The simultaneous quantization-and-fine-tuning process of L4Q is applicable to high-precision models, yielding linearly quantized weights with superior accuracy. Our experiments, conducted on the LLaMA and LLaMA2 model families using an instructional dataset, showcase L4Q's capabilities in language comprehension and few-shot in-context learning, achieving sub-4-bit precision while maintaining comparable training times to applying PEFT on a quantized model.

RepQuant: Towards Accurate Post-Training Quantization of Large Transformer Models via Scale Reparameterization

Large transformer models have demonstrated remarkable success. Post-training quantization (PTQ), which requires only a small dataset for calibration and avoids end-to-end retraining, is a promising solution for compressing these large models. Regrettably, existing PTQ methods typically exhibit non-trivial performance loss. We find that the performance bottleneck stems from over-consideration of hardware compatibility in the quantization process, compelling them to reluctantly employ simple quantizers, albeit at the expense of accuracy. With the above insights, we propose RepQuant, a novel PTQ framework with quantization-inference decoupling paradigm to address the above issues. RepQuant employs complex quantizers in the quantization process and simplified quantizers in the inference process, and performs mathematically equivalent transformations between the two through quantization scale reparameterization, thus ensuring both accurate quantization and efficient inference. More specifically, we focus on two components with extreme distributions: LayerNorm activations and Softmax activations. Initially, we apply channel-wise quantization and log2 quantization, respectively, which are tailored to their distributions. In particular, for the former, we introduce a learnable per-channel dual clipping scheme, which is designed to efficiently identify outliers in the unbalanced activations with fine granularity. Then, we reparameterize the scales to hardware-friendly layer-wise quantization and log2 quantization for inference. Moreover, quantized weight reconstruction is seamlessly integrated into the above procedure to further push the performance limits. Extensive experiments are performed on different large-scale transformer variants on multiple tasks, including vision, language, and multi-modal transformers, and RepQuant encouragingly demonstrates significant performance advantages.

Scaling Law for Quantization-Aware Training

Large language models (LLMs) demand substantial computational and memory resources, creating deployment challenges. Quantization-aware training (QAT) addresses these challenges by reducing model precision while maintaining performance. However, the scaling behavior of QAT, especially at 4-bit precision (W4A4), is not well understood. Existing QAT scaling laws often ignore key factors such as the number of training tokens and quantization granularity, which limits their applicability. This paper proposes a unified scaling law for QAT that models quantization error as a function of model size, training data volume, and quantization group size. Through 268 QAT experiments, we show that quantization error decreases as model size increases, but rises with more training tokens and coarser quantization granularity. To identify the sources of W4A4 quantization error, we decompose it into weight and activation components. Both components follow the overall trend of W4A4 quantization error, but with different sensitivities. Specifically, weight quantization error increases more rapidly with more training tokens. Further analysis shows that the activation quantization error in the FC2 layer, caused by outliers, is the primary bottleneck of W4A4 QAT quantization error. By applying mixed-precision quantization to address this bottleneck, we demonstrate that weight and activation quantization errors can converge to similar levels. Additionally, with more training data, weight quantization error eventually exceeds activation quantization error, suggesting that reducing weight quantization error is also important in such scenarios. These findings offer key insights for improving QAT research and development.

EfficientDM: Efficient Quantization-Aware Fine-Tuning of Low-Bit Diffusion Models

Diffusion models have demonstrated remarkable capabilities in image synthesis and related generative tasks. Nevertheless, their practicality for low-latency real-world applications is constrained by substantial computational costs and latency issues. Quantization is a dominant way to compress and accelerate diffusion models, where post-training quantization (PTQ) and quantization-aware training (QAT) are two main approaches, each bearing its own properties. While PTQ exhibits efficiency in terms of both time and data usage, it may lead to diminished performance in low bit-width. On the other hand, QAT can alleviate performance degradation but comes with substantial demands on computational and data resources. To capitalize on the advantages while avoiding their respective drawbacks, we introduce a data-free and parameter-efficient fine-tuning framework for low-bit diffusion models, dubbed EfficientDM, to achieve QAT-level performance with PTQ-like efficiency. Specifically, we propose a quantization-aware variant of the low-rank adapter (QALoRA) that can be merged with model weights and jointly quantized to low bit-width. The fine-tuning process distills the denoising capabilities of the full-precision model into its quantized counterpart, eliminating the requirement for training data. We also introduce scale-aware optimization and employ temporal learned step-size quantization to further enhance performance. Extensive experimental results demonstrate that our method significantly outperforms previous PTQ-based diffusion models while maintaining similar time and data efficiency. Specifically, there is only a marginal 0.05 sFID increase when quantizing both weights and activations of LDM-4 to 4-bit on ImageNet 256x256. Compared to QAT-based methods, our EfficientDM also boasts a 16.2x faster quantization speed with comparable generation quality.

Dual Grained Quantization: Efficient Fine-Grained Quantization for LLM

Large Language Models (LLMs) pose significant hardware challenges related to memory requirements and computational ability. There are two mainstream quantization schemes for LLMs: coarse-grained (e.g., channel-wise) quantization and fine-grained (e.g., group-wise) quantization. Fine-grained quantization has smaller quantization loss, consequently achieving superior performance. However, when applied to weight-activation quantization, it disrupts continuous integer matrix multiplication, leading to inefficient inference. In this paper, we introduce Dual Grained Quantization (DGQ), a novel A8W4 quantization for LLM that maintains superior performance while ensuring fast inference speed. DSQ dequantizes the fine-grained INT4 weight into coarse-grained INT8 representation and preform matrix multiplication using INT8 kernels. Besides, we develop a two-phase grid search algorithm to simplify the determination of fine-grained and coarse-grained quantization scales. We also devise a percentile clipping schema for smoothing the activation outliers without the need for complex optimization techniques. Experimental results demonstrate that DGQ consistently outperforms prior methods across various LLM architectures and a wide range of tasks. Remarkably, by our implemented efficient CUTLASS kernel, we achieve 1.12 times memory reduction and 3.24 times speed gains comparing A16W4 implementation. These advancements enable efficient deployment of A8W4 LLMs for real-world applications.

QuEST: Stable Training of LLMs with 1-Bit Weights and Activations

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining even more accurate compressed models by directly training over such representations, i.e., Quantization-Aware Training (QAT), is still open: for example, a recent study (arXiv:2411.04330v2) put the "optimal" bit-width at which models can be trained using QAT, while staying accuracy-competitive with standard FP16/BF16 precision, at 8-bits weights and activations. We advance this state-of-the-art via a new method called QuEST, which is Pareto-competitive with FP16, i.e., it provides better accuracy at lower model size, while training models with weights and activations in 4-bits or less. Moreover, QuEST allows stable training with 1-bit weights and activations. QuEST achieves this by improving two key aspects of QAT methods: (1) accurate and fast quantization of the (continuous) distributions of weights and activations via Hadamard normalization and MSE-optimal fitting; (2) a new trust gradient estimator based on the idea of explicitly minimizing the error between the noisy gradient computed over quantized states and the "true" (but unknown) full-precision gradient. Experiments on Llama-type architectures show that QuEST induces stable scaling laws across the entire range of hardware-supported precisions, and can be extended to sparse representations. We provide GPU kernel support showing that models produced by QuEST can be executed efficiently. Our code is available at https://github.com/IST-DASLab/QuEST.

PTQ1.61: Push the Real Limit of Extremely Low-Bit Post-Training Quantization Methods for Large Language Models

Large Language Models (LLMs) suffer severe performance degradation when facing extremely low-bit (sub 2-bit) quantization. Several existing sub 2-bit post-training quantization (PTQ) methods utilize a mix-precision scheme by leveraging an unstructured fine-grained mask to explicitly distinguish salient weights, while which introduces an extra 1-bit or more per weight. To explore the real limit of PTQ, we propose an extremely low-bit PTQ method called PTQ1.61, which enables weight quantization to 1.61-bit for the first time. Specifically, we first introduce a one-dimensional structured mask with negligibly additional 0.0002-bit per weight based on input activations from the perspective of reducing the upper bound of quantization error to allocate corresponding salient weight channels to 4-bit. For non-salient channels binarization, an efficient block-wise scaling factors optimization framework is then presented to take implicit row-wise correlations and angular biases into account. Different from prior works that concentrate on adjusting quantization methodologies, we further propose a novel paradigm called quantization preprocessing, where we argue that transforming the weight distribution of the pretrained model before quantization can alleviate the difficulty in per-channel extremely low-bit PTQ. Extensive experiments indicate our PTQ1.61 achieves state-of-the-art performance in extremely low-bit quantization. Codes are available at https://github.com/zjq0455/PTQ1.61.

FP4DiT: Towards Effective Floating Point Quantization for Diffusion Transformers

Diffusion Models (DM) have revolutionized the text-to-image visual generation process. However, the large computational cost and model footprint of DMs hinders practical deployment, especially on edge devices. Post-training quantization (PTQ) is a lightweight method to alleviate these burdens without the need for training or fine-tuning. While recent DM PTQ methods achieve W4A8 on integer-based PTQ, two key limitations remain: First, while most existing DM PTQ methods evaluate on classical DMs like Stable Diffusion XL, 1.5 or earlier, which use convolutional U-Nets, newer Diffusion Transformer (DiT) models like the PixArt series, Hunyuan and others adopt fundamentally different transformer backbones to achieve superior image synthesis. Second, integer (INT) quantization is prevailing in DM PTQ but doesn't align well with the network weight and activation distribution, while Floating-Point Quantization (FPQ) is still under-investigated, yet it holds the potential to better align the weight and activation distributions in low-bit settings for DiT. In response, we introduce FP4DiT, a PTQ method that leverages FPQ to achieve W4A6 quantization. Specifically, we extend and generalize the Adaptive Rounding PTQ technique to adequately calibrate weight quantization for FPQ and demonstrate that DiT activations depend on input patch data, necessitating robust online activation quantization techniques. Experimental results demonstrate that FP4DiT outperforms integer-based PTQ at W4A6 and W4A8 precision and generates convincing visual content on PixArt-alpha, PixArt-Sigma and Hunyuan in terms of several T2I metrics such as HPSv2 and CLIP.

EdgeQAT: Entropy and Distribution Guided Quantization-Aware Training for the Acceleration of Lightweight LLMs on the Edge

Despite the remarkable strides of Large Language Models (LLMs) in various fields, the wide applications of LLMs on edge devices are limited due to their massive parameters and computations. To address this, quantization is commonly adopted to generate lightweight LLMs with efficient computations and fast inference. However, Post-Training Quantization (PTQ) methods dramatically degrade in quality when quantizing weights, activations, and KV cache together to below 8 bits. Besides, many Quantization-Aware Training (QAT) works quantize model weights, leaving the activations untouched, which do not fully exploit the potential of quantization for inference acceleration on the edge. In this paper, we propose EdgeQAT, the Entropy and Distribution Guided QAT for the optimization of lightweight LLMs to achieve inference acceleration on Edge devices. We first identify that the performance drop of quantization primarily stems from the information distortion in quantized attention maps, demonstrated by the different distributions in quantized query and key of the self-attention mechanism. Then, the entropy and distribution guided QAT is proposed to mitigate the information distortion. Moreover, we design a token importance-aware adaptive method to dynamically quantize the tokens with different bit widths for further optimization and acceleration. Our extensive experiments verify the substantial improvements with our framework across various datasets. Furthermore, we achieve an on-device speedup of up to 2.37x compared with its FP16 counterparts across multiple edge devices, signaling a groundbreaking advancement.

MixDQ: Memory-Efficient Few-Step Text-to-Image Diffusion Models with Metric-Decoupled Mixed Precision Quantization

Diffusion models have achieved significant visual generation quality. However, their significant computational and memory costs pose challenge for their application on resource-constrained mobile devices or even desktop GPUs. Recent few-step diffusion models reduces the inference time by reducing the denoising steps. However, their memory consumptions are still excessive. The Post Training Quantization (PTQ) replaces high bit-width FP representation with low-bit integer values (INT4/8) , which is an effective and efficient technique to reduce the memory cost. However, when applying to few-step diffusion models, existing quantization methods face challenges in preserving both the image quality and text alignment. To address this issue, we propose an mixed-precision quantization framework - MixDQ. Firstly, We design specialized BOS-aware quantization method for highly sensitive text embedding quantization. Then, we conduct metric-decoupled sensitivity analysis to measure the sensitivity of each layer. Finally, we develop an integer-programming-based method to conduct bit-width allocation. While existing quantization methods fall short at W8A8, MixDQ could achieve W8A8 without performance loss, and W4A8 with negligible visual degradation. Compared with FP16, we achieve 3-4x reduction in model size and memory cost, and 1.45x latency speedup.

SVDQunat: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models

Diffusion models have been proven highly effective at generating high-quality images. However, as these models grow larger, they require significantly more memory and suffer from higher latency, posing substantial challenges for deployment. In this work, we aim to accelerate diffusion models by quantizing their weights and activations to 4 bits. At such an aggressive level, both weights and activations are highly sensitive, where conventional post-training quantization methods for large language models like smoothing become insufficient. To overcome this limitation, we propose SVDQuant, a new 4-bit quantization paradigm. Different from smoothing which redistributes outliers between weights and activations, our approach absorbs these outliers using a low-rank branch. We first consolidate the outliers by shifting them from activations to weights, then employ a high-precision low-rank branch to take in the weight outliers with Singular Value Decomposition (SVD). This process eases the quantization on both sides. However, na\"{\i}vely running the low-rank branch independently incurs significant overhead due to extra data movement of activations, negating the quantization speedup. To address this, we co-design an inference engine Nunchaku that fuses the kernels of the low-rank branch into those of the low-bit branch to cut off redundant memory access. It can also seamlessly support off-the-shelf low-rank adapters (LoRAs) without the need for re-quantization. Extensive experiments on SDXL, PixArt-Sigma, and FLUX.1 validate the effectiveness of SVDQuant in preserving image quality. We reduce the memory usage for the 12B FLUX.1 models by 3.5times, achieving 3.0times speedup over the 4-bit weight-only quantized baseline on the 16GB laptop 4090 GPU, paving the way for more interactive applications on PCs. Our quantization library and inference engine are open-sourced.

FireQ: Fast INT4-FP8 Kernel and RoPE-aware Quantization for LLM Inference Acceleration

As large language models become increasingly prevalent, memory bandwidth constraints significantly limit inference throughput, motivating post-training quantization (PTQ). In this paper, we propose FireQ, a co-designed PTQ framework and an INT4-FP8 matrix multiplication kernel that accelerates LLM inference across all linear layers. Specifically, FireQ quantizes linear layer weights and key-values to INT4, and activations and queries to FP8, significantly enhancing throughput. Additionally, we introduce a three-stage pipelining for the prefill phase, which modifies the FlashAttention-3 kernel, effectively reducing time-to-first-token in the prefill phase. To minimize accuracy loss from quantization, we develop novel outlier smoothing techniques tailored separately for linear and attention layers. In linear layers, we explicitly use per-tensor scaling to prevent underflow caused by the FP8 quantization scaling factor of INT4 quantization, and channel-wise scaling to compensate for coarse granularity of INT4. In attention layers, we address quantization challenges posed by rotary positional embeddings (RoPE) by combining pre-RoPE and post-RoPE scaling strategies. FireQ significantly outperforms state-of-the-art methods, achieving 1.68x faster inference in feed-forward network layers on Llama2-7B and 1.26x faster prefill phase performance on Llama3-8B compared to QServe, with negligible accuracy loss.

Learned Low Precision Graph Neural Networks

Deep Graph Neural Networks (GNNs) show promising performance on a range of graph tasks, yet at present are costly to run and lack many of the optimisations applied to DNNs. We show, for the first time, how to systematically quantise GNNs with minimal or no loss in performance using Network Architecture Search (NAS). We define the possible quantisation search space of GNNs. The proposed novel NAS mechanism, named Low Precision Graph NAS (LPGNAS), constrains both architecture and quantisation choices to be differentiable. LPGNAS learns the optimal architecture coupled with the best quantisation strategy for different components in the GNN automatically using back-propagation in a single search round. On eight different datasets, solving the task of classifying unseen nodes in a graph, LPGNAS generates quantised models with significant reductions in both model and buffer sizes but with similar accuracy to manually designed networks and other NAS results. In particular, on the Pubmed dataset, LPGNAS shows a better size-accuracy Pareto frontier compared to seven other manual and searched baselines, offering a 2.3 times reduction in model size but a 0.4% increase in accuracy when compared to the best NAS competitor. Finally, from our collected quantisation statistics on a wide range of datasets, we suggest a W4A8 (4-bit weights, 8-bit activations) quantisation strategy might be the bottleneck for naive GNN quantisations.

VPTQ: Extreme Low-bit Vector Post-Training Quantization for Large Language Models

Scaling model size significantly challenges the deployment and inference of Large Language Models (LLMs). Due to the redundancy in LLM weights, recent research has focused on pushing weight-only quantization to extremely low-bit (even down to 2 bits). It reduces memory requirements, optimizes storage costs, and decreases memory bandwidth needs during inference. However, due to numerical representation limitations, traditional scalar-based weight quantization struggles to achieve such extreme low-bit. Recent research on Vector Quantization (VQ) for LLMs has demonstrated the potential for extremely low-bit model quantization by compressing vectors into indices using lookup tables. In this paper, we introduce Vector Post-Training Quantization (VPTQ) for extremely low-bit quantization of LLMs. We use Second-Order Optimization to formulate the LLM VQ problem and guide our quantization algorithm design by solving the optimization. We further refine the weights using Channel-Independent Second-Order Optimization for a granular VQ. In addition, by decomposing the optimization problem, we propose a brief and effective codebook initialization algorithm. We also extend VPTQ to support residual and outlier quantization, which enhances model accuracy and further compresses the model. Our experimental results show that VPTQ reduces model quantization perplexity by 0.01-0.34 on LLaMA-2, 0.38-0.68 on Mistral-7B, 4.41-7.34 on LLaMA-3 over SOTA at 2-bit, with an average accuracy improvement of 0.79-1.5% on LLaMA-2, 1% on Mistral-7B, 11-22% on LLaMA-3 on QA tasks on average. We only utilize 10.4-18.6% of the quantization algorithm execution time, resulting in a 1.6-1.8times increase in inference throughput compared to SOTA.

CBQ: Cross-Block Quantization for Large Language Models

Post-training quantization (PTQ) has driven attention to producing efficient large language models (LLMs) with ultra-low costs. Since hand-craft quantization parameters lead to low performance in low-bit quantization, recent methods optimize the quantization parameters through block-wise reconstruction between the floating-point and quantized models. However, these methods suffer from two challenges: accumulated errors from independent one-by-one block quantization and reconstruction difficulties from extreme weight and activation outliers. To address these two challenges, we propose CBQ, a cross-block reconstruction-based PTQ method for LLMs. To reduce error accumulation, we introduce a cross-block dependency with the aid of a homologous reconstruction scheme to build the long-range dependency between adjacent multi-blocks with overlapping. To reduce reconstruction difficulty, we design a coarse-to-fine pre-processing (CFP) to truncate weight outliers and dynamically scale activation outliers before optimization, and an adaptive rounding scheme, called LoRA-Rounding, with two low-rank learnable matrixes to further rectify weight quantization errors. Extensive experiments demonstrate that: (1) CBQ pushes both activation and weight quantization to low-bit settings W4A4, W4A8, and W2A16. (2) CBQ achieves better performance than the existing state-of-the-art methods on various LLMs and benchmark datasets.

ZeroQuant-V2: Exploring Post-training Quantization in LLMs from Comprehensive Study to Low Rank Compensation

Post-training quantization (PTQ) has emerged as a promising technique for mitigating memory consumption and computational costs in large language models (LLMs). However, a systematic examination of various quantization schemes, model families, and quantization bit precision has been absent from the literature. In this paper, we conduct a comprehensive analysis of these factors by investigating the effects of PTQ on weight-only, activation-only, and weight-and-activation quantization using diverse methods such as round-to-nearest (RTN), GPTQ, ZeroQuant, and their variants. We apply these methods to two distinct model families with parameters ranging from 125M to 176B. Our contributions include: (1) a sensitivity analysis revealing that activation quantization is generally more susceptible to weight quantization, with smaller models often outperforming larger models in terms of activation quantization; (2) an evaluation and comparison of existing PTQ methods to optimize model size reduction while minimizing the impact on accuracy, revealing that none of the current methods can achieve the original model quality for quantization with either INT4-weight or INT4-weight-and-INT8-activation; (3) based on these insights, we propose an optimized method called Low-Rank Compensation (LoRC), which employs low-rank matrices to enhance model quality recovery with a minimal increase in model size.

Network Memory Footprint Compression Through Jointly Learnable Codebooks and Mappings

The massive interest in deep neural networks (DNNs) for both computer vision and natural language processing has been sparked by the growth in computational power. However, this led to an increase in the memory footprint, to a point where it can be challenging to simply load a model on commodity devices such as mobile phones. To address this limitation, quantization is a favored solution as it maps high precision tensors to a low precision, memory efficient format. In terms of memory footprint reduction, its most effective variants are based on codebooks. These methods, however, suffer from two limitations. First, they either define a single codebook for each tensor, or use a memory-expensive mapping to multiple codebooks. Second, gradient descent optimization of the mapping favors jumps toward extreme values, hence not defining a proximal search. In this work, we propose to address these two limitations. First, we initially group similarly distributed neurons and leverage the re-ordered structure to either apply different scale factors to the different groups, or map weights that fall in these groups to several codebooks, without any mapping overhead. Second, stemming from this initialization, we propose a joint learning of the codebook and weight mappings that bears similarities with recent gradient-based post-training quantization techniques. Third, drawing estimation from straight-through estimation techniques, we introduce a novel gradient update definition to enable a proximal search of the codebooks and their mappings. The proposed jointly learnable codebooks and mappings (JLCM) method allows a very efficient approximation of any DNN: as such, a Llama 7B can be compressed down to 2Go and loaded on 5-year-old smartphones.

Rethinking Channel Dimensions to Isolate Outliers for Low-bit Weight Quantization of Large Language Models

Large Language Models (LLMs) have recently demonstrated a remarkable success across various tasks. However, efficiently serving LLMs has been a challenge due to its large memory bottleneck, specifically in small batch inference settings (e.g. mobile devices). Weight-only quantization can be a promising approach, but sub-4 bit quantization remains a challenge due to large-magnitude activation outliers. To mitigate the undesirable outlier effect, we first propose per-IC quantization, a simple yet effective method that creates quantization groups within each input channel (IC) rather than the conventional per-output channel (OC). Our method is motivated by the observation that activation outliers affect the input dimension of the weight matrix, so similarly grouping the weights in the IC direction can isolate outliers to be within a group. We also find that activation outliers do not dictate quantization difficulty, and inherent weight sensitivities also exist. With per-IC quantization as a new outlier-friendly scheme, we then propose Adaptive Dimensions (AdaDim), a versatile quantization framework that can adapt to various weight sensitivity patterns. We demonstrate the effectiveness of AdaDim by augmenting prior methods such as Round-To-Nearest and GPTQ, showing significant improvements across various language modeling benchmarks for both base (up to +4.7% on MMLU) and instruction-tuned (up to +10% on HumanEval) LLMs.

HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks

Quantization is an effective method for reducing memory footprint and inference time of Neural Networks, e.g., for efficient inference in the cloud, especially at the edge. However, ultra low precision quantization could lead to significant degradation in model generalization. A promising method to address this is to perform mixed-precision quantization, where more sensitive layers are kept at higher precision. However, the search space for a mixed-precision quantization is exponential in the number of layers. Recent work has proposed HAWQ, a novel Hessian based framework, with the aim of reducing this exponential search space by using second-order information. While promising, this prior work has three major limitations: (i) HAWQV1 only uses the top Hessian eigenvalue as a measure of sensitivity and do not consider the rest of the Hessian spectrum; (ii) HAWQV1 approach only provides relative sensitivity of different layers and therefore requires a manual selection of the mixed-precision setting; and (iii) HAWQV1 does not consider mixed-precision activation quantization. Here, we present HAWQV2 which addresses these shortcomings. For (i), we perform a theoretical analysis showing that a better sensitivity metric is to compute the average of all of the Hessian eigenvalues. For (ii), we develop a Pareto frontier based method for selecting the exact bit precision of different layers without any manual selection. For (iii), we extend the Hessian analysis to mixed-precision activation quantization. We have found this to be very beneficial for object detection. We show that HAWQV2 achieves new state-of-the-art results for a wide range of tasks.

APQ: Joint Search for Network Architecture, Pruning and Quantization Policy

We present APQ for efficient deep learning inference on resource-constrained hardware. Unlike previous methods that separately search the neural architecture, pruning policy, and quantization policy, we optimize them in a joint manner. To deal with the larger design space it brings, a promising approach is to train a quantization-aware accuracy predictor to quickly get the accuracy of the quantized model and feed it to the search engine to select the best fit. However, training this quantization-aware accuracy predictor requires collecting a large number of quantized <model, accuracy> pairs, which involves quantization-aware finetuning and thus is highly time-consuming. To tackle this challenge, we propose to transfer the knowledge from a full-precision (i.e., fp32) accuracy predictor to the quantization-aware (i.e., int8) accuracy predictor, which greatly improves the sample efficiency. Besides, collecting the dataset for the fp32 accuracy predictor only requires to evaluate neural networks without any training cost by sampling from a pretrained once-for-all network, which is highly efficient. Extensive experiments on ImageNet demonstrate the benefits of our joint optimization approach. With the same accuracy, APQ reduces the latency/energy by 2x/1.3x over MobileNetV2+HAQ. Compared to the separate optimization approach (ProxylessNAS+AMC+HAQ), APQ achieves 2.3% higher ImageNet accuracy while reducing orders of magnitude GPU hours and CO2 emission, pushing the frontier for green AI that is environmental-friendly. The code and video are publicly available.

ZeroQuant-FP: A Leap Forward in LLMs Post-Training W4A8 Quantization Using Floating-Point Formats

In the complex domain of large language models (LLMs), striking a balance between computational efficiency and maintaining model quality is a formidable challenge. Navigating the inherent limitations of uniform quantization, particularly when dealing with outliers, and motivated by the launch of NVIDIA's H100 hardware, this study delves into the viability of floating-point (FP) quantization, particularly focusing on FP8 and FP4, as a potential solution. Our comprehensive investigation reveals that for LLMs, FP8 activation consistently outshines its integer (INT8) equivalent, with the performance edge becoming more noticeable in models possessing parameters beyond one billion. For weight quantization, our findings indicate that FP4 exhibits comparable, if not superior, performance to INT4, simplifying deployment on FP-supported hardware like H100. To mitigate the overhead from precision alignment caused by the disparity between weights and activations, we propose two scaling constraints for weight quantization that negligibly impact the performance compared to the standard W4A8 model. We additionally enhance our quantization methods by integrating the Low Rank Compensation (LoRC) strategy, yielding improvements especially in smaller models. The results of our investigation emphasize the immense potential of FP quantization for LLMs, paving the way for high-efficiency deployment in resource-limited settings.

EfficientQAT: Efficient Quantization-Aware Training for Large Language Models

Large language models (LLMs) are integral to modern natural language processing and artificial intelligence. However, they face challenges in managing their significant memory requirements. Although quantization-aware training (QAT) offers a solution by reducing memory consumption through low-bit representations with minimal accuracy loss, it demands substantial training resources to optimize model weights and quantization parameters. To address this, we propose Efficient Quantization-Aware Training (EfficientQAT), a novel quantization technique for compressing LLMs. EfficientQAT involves two consecutive phases: Block-wise training of all parameters (Block-AP) and end-to-end training of quantization parameters (E2E-QP). Block-AP sequentially conducts quantization-aware training for all parameters in each transformer block with block-wise reconstruction, maintaining efficiency by avoiding training the entire LLM. Initialized with quantized model, E2E-QP then trains only quantization parameters (step sizes) end-to-end, enhancing efficiency with a fixed quantized backbone and reduced trainable parameter count. Extensive experiments demonstrate that EfficientQAT outperforms previous quantization methods across a range of models, including base LLMs, instruction-tuned LLMs, and multimodal LLMs, with scales from 7B to 70B parameters at various quantization bits. For instance, EfficientQAT obtains a 2-bit Llama-2-70B model on a single A100-80GB GPU in 41 hours, with less than 3\% accuracy degradation compared to the full precision (69.48 vs. 72.41). Notably, this INT2 quantized 70B model obtains a 1.67 accuracy gain over the Llama-2-13B model (69.48 vs. 67.81) while requiring less memory (19.2GB vs. 24.2GB). Code is available at https://github.com/OpenGVLab/EfficientQAT.

"Give Me BF16 or Give Me Death"? Accuracy-Performance Trade-Offs in LLM Quantization

Despite the popularity of large language model (LLM) quantization for inference acceleration, significant uncertainty remains regarding the accuracy-performance trade-offs associated with various quantization formats. We present a comprehensive empirical study of quantized accuracy, evaluating popular quantization formats (FP8, INT8, INT4) across academic benchmarks and real-world tasks, on the entire Llama-3.1 model family. Additionally, our study examines the difference in text generated by quantized models versus their uncompressed counterparts. Beyond benchmarks, we also present a couple of quantization improvements which allowed us to obtain state-of-the-art accuracy recovery results. Our investigation, encompassing over 500,000 individual evaluations, yields several key findings: (1) FP8 weight and activation quantization (W8A8-FP) is lossless across all model scales, (2) INT8 weight and activation quantization (W8A8-INT), when properly tuned, incurs surprisingly low 1-3% accuracy degradation, and (3) INT4 weight-only quantization (W4A16-INT) is competitive with 8-bit integer weight and activation quantization. To address the question of the "best" format for a given deployment environment, we conduct inference performance analysis using the popular open-source vLLM framework on various GPU architectures. We find that W4A16 offers the best cost-efficiency for synchronous deployments, and for asynchronous deployment on mid-tier GPUs. At the same time, W8A8 formats excel in asynchronous "continuous batching" deployment of mid- and large-size models on high-end GPUs. Our results provide a set of practical guidelines for deploying quantized LLMs across scales and performance requirements.

AffineQuant: Affine Transformation Quantization for Large Language Models

The significant resource requirements associated with Large-scale Language Models (LLMs) have generated considerable interest in the development of techniques aimed at compressing and accelerating neural networks. Among these techniques, Post-Training Quantization (PTQ) has emerged as a subject of considerable interest due to its noteworthy compression efficiency and cost-effectiveness in the context of training. Existing PTQ methods for LLMs limit the optimization scope to scaling transformations between pre- and post-quantization weights. In this paper, we advocate for the direct optimization using equivalent Affine transformations in PTQ (AffineQuant). This approach extends the optimization scope and thus significantly minimizing quantization errors. Additionally, by employing the corresponding inverse matrix, we can ensure equivalence between the pre- and post-quantization outputs of PTQ, thereby maintaining its efficiency and generalization capabilities. To ensure the invertibility of the transformation during optimization, we further introduce a gradual mask optimization method. This method initially focuses on optimizing the diagonal elements and gradually extends to the other elements. Such an approach aligns with the Levy-Desplanques theorem, theoretically ensuring invertibility of the transformation. As a result, significant performance improvements are evident across different LLMs on diverse datasets. To illustrate, we attain a C4 perplexity of 15.76 (2.26 lower vs 18.02 in OmniQuant) on the LLaMA2-7B model of W4A4 quantization without overhead. On zero-shot tasks, AffineQuant achieves an average of 58.61 accuracy (1.98 lower vs 56.63 in OmniQuant) when using 4/4-bit quantization for LLaMA-30B, which setting a new state-of-the-art benchmark for PTQ in LLMs.

EasyQuant: An Efficient Data-free Quantization Algorithm for LLMs

Large language models (LLMs) have proven to be very superior to conventional methods in various tasks. However, their expensive computations and high memory requirements are prohibitive for deployment. Model quantization is an effective method for reducing this overhead. The problem is that in most previous works, the quantized model was calibrated using few samples from the training data, which might affect the generalization of the quantized LLMs to unknown cases and tasks. Hence in this work, we explore an important question: Can we design a data-independent quantization method for LLMs to guarantee its generalization performance? In this work, we propose EasyQuant, a training-free and data-independent weight-only quantization algorithm for LLMs. Our observation indicates that two factors: outliers in the weight and quantization ranges, are essential for reducing the quantization error. Therefore, in EasyQuant, we leave the outliers (less than 1%) unchanged and optimize the quantization range to reduce the reconstruction error. With these methods, we surprisingly find that EasyQuant achieves comparable performance to the original model. Since EasyQuant does not depend on any training data, the generalization performance of quantized LLMs is safely guaranteed. Moreover, EasyQuant can be implemented in parallel so that the quantized model could be attained in a few minutes even for LLMs over 100B. To our best knowledge, we are the first work that achieves almost lossless quantization performance for LLMs under a data-independent setting and our algorithm runs over 10 times faster than the data-dependent methods.

Low-Rank Quantization-Aware Training for LLMs

Large language models (LLMs) are omnipresent, however their practical deployment is challenging due to their ever increasing computational and memory demands. Quantization is one of the most effective ways to make them more compute and memory efficient. Quantization-aware training (QAT) methods, generally produce the best quantized performance, however it comes at the cost of potentially long training time and excessive memory usage, making it impractical when applying for LLMs. Inspired by parameter-efficient fine-tuning (PEFT) and low-rank adaptation (LoRA) literature, we propose LR-QAT -- a lightweight and memory-efficient QAT algorithm for LLMs. LR-QAT employs several components to save memory without sacrificing predictive performance: (a) low-rank auxiliary weights that are aware of the quantization grid; (b) a downcasting operator using fixed-point or double-packed integers and (c) checkpointing. Unlike most related work, our method (i) is inference-efficient, leading to no additional overhead compared to traditional PTQ; (ii) can be seen as a general extended pretraining framework, meaning that the resulting model can still be utilized for any downstream task afterwards; (iii) can be applied across a wide range of quantization settings, such as different choices quantization granularity, activation quantization, and seamlessly combined with many PTQ techniques. We apply LR-QAT to LLaMA-1/2/3 and Mistral model families and validate its effectiveness on several downstream tasks. Our method outperforms common post-training quantization (PTQ) approaches and reaches the same model performance as full-model QAT at the fraction of its memory usage. Specifically, we can train a 7B LLM on a single consumer grade GPU with 24GB of memory. Our source code is available at https://github.com/qualcomm-ai-research/LR-QAT

Pareto-Optimal Quantized ResNet Is Mostly 4-bit

Quantization has become a popular technique to compress neural networks and reduce compute cost, but most prior work focuses on studying quantization without changing the network size. Many real-world applications of neural networks have compute cost and memory budgets, which can be traded off with model quality by changing the number of parameters. In this work, we use ResNet as a case study to systematically investigate the effects of quantization on inference compute cost-quality tradeoff curves. Our results suggest that for each bfloat16 ResNet model, there are quantized models with lower cost and higher accuracy; in other words, the bfloat16 compute cost-quality tradeoff curve is Pareto-dominated by the 4-bit and 8-bit curves, with models primarily quantized to 4-bit yielding the best Pareto curve. Furthermore, we achieve state-of-the-art results on ImageNet for 4-bit ResNet-50 with quantization-aware training, obtaining a top-1 eval accuracy of 77.09%. We demonstrate the regularizing effect of quantization by measuring the generalization gap. The quantization method we used is optimized for practicality: It requires little tuning and is designed with hardware capabilities in mind. Our work motivates further research into optimal numeric formats for quantization, as well as the development of machine learning accelerators supporting these formats. As part of this work, we contribute a quantization library written in JAX, which is open-sourced at https://github.com/google-research/google-research/tree/master/aqt.

Efficient Personalization of Quantized Diffusion Model without Backpropagation

Diffusion models have shown remarkable performance in image synthesis, but they demand extensive computational and memory resources for training, fine-tuning and inference. Although advanced quantization techniques have successfully minimized memory usage for inference, training and fine-tuning these quantized models still require large memory possibly due to dequantization for accurate computation of gradients and/or backpropagation for gradient-based algorithms. However, memory-efficient fine-tuning is particularly desirable for applications such as personalization that often must be run on edge devices like mobile phones with private data. In this work, we address this challenge by quantizing a diffusion model with personalization via Textual Inversion and by leveraging a zeroth-order optimization on personalization tokens without dequantization so that it does not require gradient and activation storage for backpropagation that consumes considerable memory. Since a gradient estimation using zeroth-order optimization is quite noisy for a single or a few images in personalization, we propose to denoise the estimated gradient by projecting it onto a subspace that is constructed with the past history of the tokens, dubbed Subspace Gradient. In addition, we investigated the influence of text embedding in image generation, leading to our proposed time steps sampling, dubbed Partial Uniform Timestep Sampling for sampling with effective diffusion timesteps. Our method achieves comparable performance to prior methods in image and text alignment scores for personalizing Stable Diffusion with only forward passes while reducing training memory demand up to 8.2times.

QLLM: Accurate and Efficient Low-Bitwidth Quantization for Large Language Models

Large Language Models (LLMs) excel in NLP, but their demands hinder their widespread deployment. While Quantization-Aware Training (QAT) offers a solution, its extensive training costs make Post-Training Quantization (PTQ) a more practical approach for LLMs. In existing studies, activation outliers in particular channels are identified as the bottleneck to PTQ accuracy. They propose to transform the magnitudes from activations to weights, which however offers limited alleviation or suffers from unstable gradients, resulting in a severe performance drop at low-bitwidth. In this paper, we propose QLLM, an accurate and efficient low-bitwidth PTQ method designed for LLMs. QLLM introduces an adaptive channel reassembly technique that reallocates the magnitude of outliers to other channels, thereby mitigating their impact on the quantization range. This is achieved by channel disassembly and channel assembly, which first breaks down the outlier channels into several sub-channels to ensure a more balanced distribution of activation magnitudes. Then similar channels are merged to maintain the original channel number for efficiency. Additionally, an adaptive strategy is designed to autonomously determine the optimal number of sub-channels for channel disassembly. To further compensate for the performance loss caused by quantization, we propose an efficient tuning method that only learns a small number of low-rank weights while freezing the pre-trained quantized model. After training, these low-rank parameters can be fused into the frozen weights without affecting inference. Extensive experiments on LLaMA-1 and LLaMA-2 show that QLLM can obtain accurate quantized models efficiently. For example, QLLM quantizes the 4-bit LLaMA-2-70B within 10 hours on a single A100-80G GPU, outperforming the previous state-of-the-art method by 7.89% on the average accuracy across five zero-shot tasks.

OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models

Large language models (LLMs) have revolutionized natural language processing tasks. However, their practical deployment is hindered by their immense memory and computation requirements. Although recent post-training quantization (PTQ) methods are effective in reducing memory footprint and improving the computational efficiency of LLM, they hand-craft quantization parameters, which leads to low performance and fails to deal with extremely low-bit quantization. To tackle this issue, we introduce an Omnidirectionally calibrated Quantization (OmniQuant) technique for LLMs, which achieves good performance in diverse quantization settings while maintaining the computational efficiency of PTQ by efficiently optimizing various quantization parameters. OmniQuant comprises two innovative components including Learnable Weight Clipping (LWC) and Learnable Equivalent Transformation (LET). LWC modulates the extreme values of weights by optimizing the clipping threshold. Meanwhile, LET tackles activation outliers by shifting the challenge of quantization from activations to weights through a learnable equivalent transformation. Operating within a differentiable framework using block-wise error minimization, OmniQuant can optimize the quantization process efficiently for both weight-only and weight-activation quantization. For instance, the LLaMA-2 model family with the size of 7-70B can be processed with OmniQuant on a single A100-40G GPU within 1-16 hours using 128 samples. Extensive experiments validate OmniQuant's superior performance across diverse quantization configurations such as W4A4, W6A6, W4A16, W3A16, and W2A16. Additionally, OmniQuant demonstrates effectiveness in instruction-tuned models and delivers notable improvements in inference speed and memory reduction on real devices. Codes and models are available at https://github.com/OpenGVLab/OmniQuant.

LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Models

Recent advances in self-supervised learning and the Transformer architecture have significantly improved natural language processing (NLP), achieving remarkably low perplexity. However, the growing size of NLP models introduces a memory wall problem during the generation phase. To mitigate this issue, recent efforts have focused on quantizing model weights to sub-4-bit precision while preserving full precision for activations, resulting in practical speed-ups during inference on a single GPU. However, these improvements primarily stem from reduced memory movement, which necessitates a resource-intensive dequantization process rather than actual computational reduction. In this paper, we introduce LUT-GEMM, an efficient kernel for quantized matrix multiplication, which not only eliminates the resource-intensive dequantization process but also reduces computational costs compared to previous kernels for weight-only quantization. Furthermore, we proposed group-wise quantization to offer a flexible trade-off between compression ratio and accuracy. The impact of LUT-GEMM is facilitated by implementing high compression ratios through low-bit quantization and efficient LUT-based operations. We show experimentally that when applied to the OPT-175B model with 3-bit quantization, LUT-GEMM substantially accelerates token generation latency, achieving a remarkable 2.1times improvement on a single GPU when compared to OPTQ, which relies on the costly dequantization process.

FlexRound: Learnable Rounding based on Element-wise Division for Post-Training Quantization

Post-training quantization (PTQ) has been gaining popularity for the deployment of deep neural networks on resource-limited devices since unlike quantization-aware training, neither a full training dataset nor end-to-end training is required at all. As PTQ schemes based on reconstructing each layer or block output turn out to be effective to enhance quantized model performance, recent works have developed algorithms to devise and learn a new weight-rounding scheme so as to better reconstruct each layer or block output. In this work, we propose a simple yet effective new weight-rounding mechanism for PTQ, coined FlexRound, based on element-wise division instead of typical element-wise addition such that FlexRound enables jointly learning a common quantization grid size as well as a different scale for each pre-trained weight. Thanks to the reciprocal rule of derivatives induced by element-wise division, FlexRound is inherently able to exploit pre-trained weights when updating their corresponding scales, and thus, flexibly quantize pre-trained weights depending on their magnitudes. We empirically validate the efficacy of FlexRound on a wide range of models and tasks. To the best of our knowledge, our work is the first to carry out comprehensive experiments on not only image classification and natural language understanding but also natural language generation, assuming a per-tensor uniform PTQ setting. Moreover, we demonstrate, for the first time, that large language models can be efficiently quantized, with only a negligible impact on performance compared to half-precision baselines, achieved by reconstructing the output in a block-by-block manner.

SageAttention2 Technical Report: Accurate 4 Bit Attention for Plug-and-play Inference Acceleration

Although quantization for linear layers has been widely used, its application to accelerate the attention process remains limited. SageAttention utilizes 8-bit matrix multiplication, 16-bit matrix multiplication with 16-bit accumulator, and precision-enhancing methods, implementing an accurate and 2x speedup kernel compared to FlashAttention2. To further enhance the efficiency of attention computation while maintaining precision, we propose SageAttention2, which utilizes significantly faster 4-bit matrix multiplication (Matmul) alongside additional precision-enhancing techniques. First, we propose to quantize matrixes (Q, K) to INT4 in a warp-level granularity and quantize matrixes (widetilde P, V) to FP8. Second, we propose a method to smooth Q and V, enhancing the accuracy of attention with INT4 QK and FP8 PV. Third, we analyze the quantization accuracy across timesteps and layers, then propose an adaptive quantization method to ensure the end-to-end metrics over various models. The operations per second (OPS) of SageAttention2 surpass FlashAttention2 and xformers by about 3x and 5x on RTX4090, respectively. Comprehensive experiments confirm that our approach incurs negligible end-to-end metrics loss across diverse models, including those for large language processing, image generation, and video generation. The codes are available at https://github.com/thu-ml/SageAttention.

EAQuant: Enhancing Post-Training Quantization for MoE Models via Expert-Aware Optimization

Mixture-of-Experts (MoE) models have emerged as a cornerstone of large-scale deep learning by efficiently distributing computation and enhancing performance. However, their unique architecture-characterized by sparse expert activation and dynamic routing mechanisms-introduces inherent complexities that challenge conventional quantization techniques. Existing post-training quantization (PTQ) methods struggle to address activation outliers, router consistency and sparse expert calibration, leading to significant performance degradation. To bridge this gap, we propose EAQuant, a novel PTQ framework tailored for MoE architectures. Our method systematically tackles these challenges through three key innovations: (1) expert-aware smoothing aggregation to suppress activation outliers and stabilize quantization, (2) router logits distribution alignment to preserve expert selection consistency post-quantization, and (3) expert-level calibration data balance to optimize sparsely activated experts. Extensive experiments across W4A4 and extreme W3A4 quantization configurations demonstrate that EAQuant significantly outperforms existing methods, achieving average score improvements of 1.15 - 2.28% across three diverse MoE architectures, with particularly pronounced gains in reasoning tasks and robust performance retention under aggressive quantization. By integrating these innovations, EAQuant establishes a new state-of-the-art for high-precision, efficient MoE model compression. Our code is available at https://github.com/darren-fzq/EAQuant.

MobileQuant: Mobile-friendly Quantization for On-device Language Models

Large language models (LLMs) have revolutionized language processing, delivering outstanding results across multiple applications. However, deploying LLMs on edge devices poses several challenges with respect to memory, energy, and compute costs, limiting their widespread use in devices such as mobile phones. A promising solution is to reduce the number of bits used to represent weights and activations. While existing works have found partial success at quantizing LLMs to lower bitwidths, e.g. 4-bit weights, quantizing activations beyond 16 bits often leads to large computational overheads due to poor on-device quantization support, or a considerable accuracy drop. Yet, 8-bit activations are very attractive for on-device deployment as they would enable LLMs to fully exploit mobile-friendly hardware, e.g. Neural Processing Units (NPUs). In this work, we make a first attempt to facilitate the on-device deployment of LLMs using integer-only quantization. We first investigate the limitations of existing quantization methods for on-device deployment, with a special focus on activation quantization. We then address these limitations by introducing a simple post-training quantization method, named MobileQuant, that extends previous weight equivalent transformation works by jointly optimizing the weight transformation and activation range parameters in an end-to-end manner. MobileQuant demonstrates superior capabilities over existing methods by 1) achieving near-lossless quantization on a wide range of LLM benchmarks, 2) reducing latency and energy consumption by 20\%-50\% compared to current on-device quantization strategies, 3) requiring limited compute budget, 4) being compatible with mobile-friendly compute units, e.g. NPU.

SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models

Large language models (LLMs) achieve remarkable performance in natural language understanding but require substantial computation and memory resources. Post-training quantization (PTQ) is a powerful compression technique extensively investigated in LLMs. However, existing PTQ methods are still not ideal in terms of accuracy and efficiency, especially with below 4 bit-widths. Standard PTQ methods using group-wise quantization suffer difficulties in quantizing LLMs accurately to such low-bit, but advanced methods remaining high-precision weights element-wisely are hard to realize their theoretical hardware efficiency. This paper presents a Salience-Driven Mixed-Precision Quantization scheme for LLMs, namely SliM-LLM. The scheme exploits the salience distribution of weights to determine optimal bit-width and quantizers for accurate LLM quantization, while aligning bit-width partition to groups for compact memory usage and fast integer inference. Specifically, the proposed SliM-LLM mainly relies on two novel techniques: (1) Salience-Determined Bit Allocation utilizes the clustering characteristics of salience distribution to allocate the bit-widths of each group, increasing the accuracy of quantized LLMs and maintaining the inference efficiency; (2) Salience-Weighted Quantizer Calibration optimizes the parameters of the quantizer by considering the element-wise salience within the group, balancing the maintenance of salient information and minimization of errors. Comprehensive experiments show that SliM-LLM significantly improves the accuracy of LLMs at ultra-low bits, e.g., 2-bit LLaMA-7B achieves a 5.5-times memory-saving than original model on NVIDIA A800 GPUs, and 48% decrease of perplexity compared to the state-of-the-art gradient-free PTQ method. Moreover, SliM-LLM+, which is integrated from the extension of SliM-LLM with gradient-based quantizers, further reduces perplexity by 35.1%.

DopQ-ViT: Towards Distribution-Friendly and Outlier-Aware Post-Training Quantization for Vision Transformers

Vision transformers (ViTs) have garnered significant attention for their performance in vision tasks, but the high computational cost and significant latency issues have hindered widespread adoption. Post-training quantization (PTQ), a promising method for model compression, still faces accuracy degradation challenges with ViTs. There are two reasons for this: the existing quantization paradigm does not fit the power-law distribution of post-Softmax activations well, and accuracy inevitably decreases after reparameterizing post-LayerNorm activations. We propose a Distribution-Friendly and Outlier-Aware Post-training Quantization method for Vision Transformers, named DopQ-ViT. DopQ-ViT analyzes the inefficiencies of current quantizers and introduces a distribution-friendly Tan Quantizer called TanQ. TanQ focuses more on values near 1, more accurately preserving the power-law distribution of post-Softmax activations, and achieves favorable results. Besides, during the reparameterization of post-LayerNorm activations from channel-wise to layer-wise quantization, the accuracy degradation is mainly due to the significant impact of outliers in the scaling factors. Therefore, DopQ-ViT proposes a method to select Median as the Optimal Scaling Factor, denoted as MOSF, which compensates for the influence of outliers and preserves the performance of the quantization model. DopQ-ViT has been extensively validated and significantly improves the performance of quantization models, especially in low-bit settings.

Enhancing Ultra-Low-Bit Quantization of Large Language Models Through Saliency-Aware Partial Retraining

Large language models offer remarkable capabilities, but their size and computational demands pose practical challenges. Quantization methods compress their size through replacing their high-precision parameters by quantized values of lower precision. Post-training quantization reduces model size efficiently at the cost of decreased accuracy, while quantization-aware training better preserves accuracy but is resource-intensive. Among existing post-training quantization algorithms, the ApiQ method achieves superior accuracy preservation at minimal memory and time overhead. We investigate two ideas to extend performance in ultra-low-bit quantization beyond ApiQ's level. First, we look into combining existing quantization-aware training techniques with ApiQ's partial training. We show that this does not outperform the baseline ApiQ method with limited training data and frozen weights. This leads to two key insights: (1) The substantial representational capacity that is gained through full retraining may not be feasible through partial training. (2) This gain seems to depend on using a large and diverse dataset in quantization-aware training. Second, through a novel approach informed by the two insights, we propose an ultra-low-bit quantization method that builds upon ApiQ and extends its performance without the need for full retraining. It relies on a saliency-aware regularization term that prioritizes preserving the most impactful parameters during quantization. Our experiments on benchmark language models from the LLaMA family show that our proposed approach boosts accuracy and tightens the gap between the quantized model and the full-precision model, with minimal overhead. Our method will be made publicly available to facilitate future developments in ultra-low-bit quantization of large language models.

ZeroQ: A Novel Zero Shot Quantization Framework

Quantization is a promising approach for reducing the inference time and memory footprint of neural networks. However, most existing quantization methods require access to the original training dataset for retraining during quantization. This is often not possible for applications with sensitive or proprietary data, e.g., due to privacy and security concerns. Existing zero-shot quantization methods use different heuristics to address this, but they result in poor performance, especially when quantizing to ultra-low precision. Here, we propose ZeroQ , a novel zero-shot quantization framework to address this. ZeroQ enables mixed-precision quantization without any access to the training or validation data. This is achieved by optimizing for a Distilled Dataset, which is engineered to match the statistics of batch normalization across different layers of the network. ZeroQ supports both uniform and mixed-precision quantization. For the latter, we introduce a novel Pareto frontier based method to automatically determine the mixed-precision bit setting for all layers, with no manual search involved. We extensively test our proposed method on a diverse set of models, including ResNet18/50/152, MobileNetV2, ShuffleNet, SqueezeNext, and InceptionV3 on ImageNet, as well as RetinaNet-ResNet50 on the Microsoft COCO dataset. In particular, we show that ZeroQ can achieve 1.71\% higher accuracy on MobileNetV2, as compared to the recently proposed DFQ method. Importantly, ZeroQ has a very low computational overhead, and it can finish the entire quantization process in less than 30s (0.5\% of one epoch training time of ResNet50 on ImageNet). We have open-sourced the ZeroQ frameworkhttps://github.com/amirgholami/ZeroQ.

Layer-Wise Quantization: A Pragmatic and Effective Method for Quantizing LLMs Beyond Integer Bit-Levels

We present a simple meta quantization approach that quantizes different layers of a large language model (LLM) at different bit levels, and is independent of the underlying quantization technique. Specifically, we quantize the most important layers to higher bit precision and less important layers to lower bits. We propose two effective strategies to measure the importance of layers within LLMs: the first measures the importance of a layer based on how different its output embeddings are from the input embeddings (higher is better); the second estimates the importance of a layer using the number of layer weights that are much larger than average (smaller is better). We show that quantizing different layers at varying bits according to our importance scores results in minimal performance drop with a far more compressed model size. Finally, we present several practical key takeaways from our variable layer-wise quantization experiments: (a) LLM performance under variable quantization remains close to the original model until 25-50% of layers are moved in lower quantization using our proposed ordering but only until 5-10% if moved using no specific ordering; (b) Adding layer importance to inherently dynamic quantization techniques can further improve their performance, showing that our approach is complementary to other dynamic quantization methods; (c) Quantizing LLMs to lower bits performs substantially better than pruning unless extreme quantization (2-bit) is used; and (d) Layer-wise quantization to lower bits works better in the case of larger LLMs with more layers compared to smaller LLMs with fewer layers. Our code is publicly available at https://github.com/RazvanDu/LayerwiseQuant/.

Post-Training Quantization with Low-precision Minifloats and Integers on FPGAs

Post-Training Quantization (PTQ) is a powerful technique for model compression, reducing the precision of neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point quantization (FP8) in the context of PTQ for model inference. However, the exploration of floating-point formats smaller than 8 bits and their comparison with integer quantization remains relatively limited. In this work, we present minifloats, which are reduced-precision floating-point formats capable of further reducing the memory footprint, latency, and energy cost of a model while approaching full-precision model accuracy. Our work presents a novel PTQ design-space exploration, comparing minifloat and integer quantization schemes across a range of 3 to 8 bits for both weights and activations. We examine the applicability of various PTQ techniques to minifloats, including weight equalization, bias correction, SmoothQuant, gradient-based learned rounding, and the GPTQ method. Our experiments validate the effectiveness of low-precision minifloats when compared to their integer counterparts across a spectrum of accuracy-precision trade-offs on a set of reference deep learning vision workloads. Finally, we evaluate our results against an FPGA-based hardware cost model, showing that integer quantization often remains the Pareto-optimal option, given its relatively smaller hardware resource footprint.

LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning

We propose a simple approach for memory-efficient adaptation of pretrained language models. Our approach uses an iterative algorithm to decompose each pretrained matrix into a high-precision low-rank component and a memory-efficient quantized component. During finetuning, the quantized component remains fixed and only the low-rank component is updated. We present an integer linear programming formulation of the quantization component which enables dynamic configuration of quantization parameters (e.g., bit-width, block size) for each matrix given an overall target memory budget. We further explore a data-aware version of the algorithm which uses an approximation of the Fisher information matrix to weight the reconstruction objective during matrix decomposition. Experiments on adapting RoBERTa and LLaMA-2 (7B and 70B) demonstrate that our low-rank plus quantized matrix decomposition approach (LQ-LoRA) outperforms strong QLoRA and GPTQ-LoRA baselines and moreover enables more aggressive quantization. For example, on the OpenAssistant benchmark LQ-LoRA is able to learn a 2.5-bit LLaMA-2 model that is competitive with a model finetuned with 4-bit QLoRA. When finetuned on a language modeling calibration dataset, LQ-LoRA can also be used for model compression; in this setting our 2.75-bit LLaMA-2-70B model (which has 2.85 bits on average when including the low-rank components and requires 27GB of GPU memory) is competitive with the original model in full precision.

CPTQuant - A Novel Mixed Precision Post-Training Quantization Techniques for Large Language Models

Large language models have transformed the comprehension and generation of natural language tasks, but they come with substantial memory and computational requirements. Quantization techniques have emerged as a promising avenue for addressing these challenges while preserving accuracy and making energy efficient. We propose CPTQuant, a comprehensive strategy that introduces correlation-based (CMPQ), pruning-based (PMPQ), and Taylor decomposition-based (TDMPQ) mixed precision techniques. CMPQ adapts the precision level based on canonical correlation analysis of different layers. PMPQ optimizes precision layer-wise based on their sensitivity to sparsity. TDMPQ modifies precision using Taylor decomposition to assess each layer's sensitivity to input perturbation. These strategies allocate higher precision to more sensitive layers while diminishing precision to robust layers. CPTQuant assesses the performance across BERT, OPT-125M, OPT-350M, OPT-1.3B, and OPT-2.7B. We demonstrate up to 4x compression and a 2x-fold increase in efficiency with minimal accuracy drop compared to Hugging Face FP16. PMPQ stands out for achieving a considerably higher model compression. Sensitivity analyses across various LLMs show that the initial and final 30% of layers exhibit higher sensitivities than the remaining layers. PMPQ demonstrates an 11% higher compression ratio than other methods for classification tasks, while TDMPQ achieves a 30% greater compression ratio for language modeling tasks.

PB-LLM: Partially Binarized Large Language Models

This paper explores network binarization, a radical form of quantization, compressing model weights to a single bit, specifically for Large Language Models (LLMs) compression. Due to previous binarization methods collapsing LLMs, we propose a novel approach, Partially-Binarized LLM (PB-LLM), which can achieve extreme low-bit quantization while maintaining the linguistic reasoning capacity of quantized LLMs. Specifically, our exploration first uncovers the ineffectiveness of naive applications of existing binarization algorithms and highlights the imperative role of salient weights in achieving low-bit quantization. Thus, PB-LLM filters a small ratio of salient weights during binarization, allocating them to higher-bit storage, i.e., partially-binarization. PB-LLM is extended to recover the capacities of quantized LMMs, by analyzing from the perspective of post-training quantization (PTQ) and quantization-aware training (QAT). Under PTQ, combining the concepts from GPTQ, we reconstruct the binarized weight matrix guided by the Hessian matrix and successfully recover the reasoning capacity of PB-LLM in low-bit. Under QAT, we freeze the salient weights during training, explore the derivation of optimal scaling factors crucial for minimizing the quantization error, and propose a scaling mechanism based on this derived scaling strategy for residual binarized weights. Those explorations and the developed methodologies significantly contribute to rejuvenating the performance of low-bit quantized LLMs and present substantial advancements in the field of network binarization for LLMs.The code is available at https://github.com/hahnyuan/BinaryLLM.

Augmenting Hessians with Inter-Layer Dependencies for Mixed-Precision Post-Training Quantization

Efficiently serving neural network models with low latency is becoming more challenging due to increasing model complexity and parameter count. Model quantization offers a solution which simultaneously reduces memory footprint and compute requirements. However, aggressive quantization may lead to an unacceptable loss in model accuracy owing to differences in sensitivity to numerical imperfection across different layers in the model. To address this challenge, we propose a mixed-precision post training quantization (PTQ) approach that assigns different numerical precisions to tensors in a network based on their specific needs, for a reduced memory footprint and improved latency while preserving model accuracy. Previous works rely on layer-wise Hessian information to determine numerical precision, but as we demonstrate, Hessian estimation is typically insufficient in determining an effective ordering of layer sensitivities. We address this by augmenting the estimated Hessian with additional information to capture inter-layer dependencies. We demonstrate that this consistently improves PTQ performance along the accuracy-latency Pareto frontier across multiple models. Our method combines second-order information and inter-layer dependencies to guide a bisection search, finding quantization configurations within a user-configurable model accuracy degradation range. We evaluate the effectiveness of our method on the ResNet50, MobileNetV2, and BERT models. Our experiments demonstrate latency reductions compared to a 16-bit baseline of 25.48%, 21.69%, and 33.28% respectively, while maintaining model accuracy to within 99.99% of the baseline model.

COMET: Towards Partical W4A4KV4 LLMs Serving

Quantization is a widely-used compression technology to reduce the overhead of serving large language models (LLMs) on terminal devices and in cloud data centers. However, prevalent quantization methods, such as 8-bit weight-activation or 4-bit weight-only quantization, achieve limited performance improvements due to poor support for low-precision (e.g., 4-bit) activation. This work, for the first time, realizes practical W4A4KV4 serving for LLMs, fully utilizing the INT4 tensor cores on modern GPUs and reducing the memory bottleneck caused by the KV cache. Specifically, we propose a novel fine-grained mixed-precision quantization algorithm (FMPQ) that compresses most activations into 4-bit with negligible accuracy loss. To support mixed-precision matrix multiplication for W4A4 and W4A8, we develop a highly optimized W4Ax kernel. Our approach introduces a novel mixed-precision data layout to facilitate access and fast dequantization for activation and weight tensors, utilizing the GPU's software pipeline to hide the overhead of data loading and conversion. Additionally, we propose fine-grained streaming multiprocessor (SM) scheduling to achieve load balance across different SMs. We integrate the optimized W4Ax kernel into our inference framework, COMET, and provide efficient management to support popular LLMs such as LLaMA-3-70B. Extensive evaluations demonstrate that, when running LLaMA family models on a single A100-80G-SMX4, COMET achieves a kernel-level speedup of 2.88times over cuBLAS and a 2.02 times throughput improvement compared to TensorRT-LLM from an end-to-end framework perspective.

OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.