Daily Papers

Document manipulation localization models achieve strong performance on public benchmarks yet fail to generalize to operational document workflows. We identify a critical and overlooked source of this gap: the mismatch between the narrow distribution of JPEG quantization tables used during training -restricted to standard libjpeg quality factors -and the heterogeneous compression profiles encountered in real-world insurance document pipelines. To isolate this factor, we conduct a controlled factorial study comparing two architectures with contrasting levels of quantization table awareness -FFDN [2] and Mesorch [20] -each trained under either standard quality factor augmentation (Standard-QT ) or operationally calibrated quantization tables sampled from DocQT, a quantization-table bank derived from a MAIF operational image corpus (Real-QT ), and evaluated under three recompression conditions. Training under Real-QT yields substantial localization gains on DocTamper [15] and significantly reduces the pixel-level false positive rate on authentic operational documents, but only for architectures that explicitly ingest the quantization table as input. The released DocQT quantization-table dataset and compression-reproduction material are directly available at https://github.com/Kyliroco/Improving-Document-Forgery-Localization-Robustness-via-Diverse-JPEG-Quantization-Tables. These results demonstrate that standard quality factor augmentation does not adequately proxy operational compression diversity, and that architectural choices explicitly conditioning on the quantization table provide a meaningful robustness advantage for real-world deployment.

We present any4, a learned 4-bit weight quantization solution for large language models (LLMs) providing arbitrary numeric representations without requiring pre-processing of weights or activations. any4 yields higher accuracy compared to other related 4-bit numeric representation types: int4, fp4 and nf4, as evaluated on a range of model sizes, generations and families (Llama 2, Llama 3, Mistral and Mixtral). While any4 does not require preprocessing of weights or activations, it is also competitive with orthogonal techniques that require such preprocessing (e.g., AWQ and GPTQ). We also experiment with any3 and any2 and show competitiveness at lower bits. Additionally, we show that we can calibrate using a single curated diverse sample rather than hundreds of samples from a dataset as done in most quantization approaches. We also open source tinygemm, a latency optimized GPU matrix multiplication library for LLMs, that implements any4 using a GPU-efficient lookup table strategy along with other common quantization methods. We open source our code at https://github.com/facebookresearch/any4 .

Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations' dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer separately by optimizing its parameters over the calibration set. We empirically demonstrate that this approach is: (1) much less susceptible to over-fitting than the standard fine-tuning approaches, and can be used even on a very small calibration set; and (2) more powerful than previous methods, which only set the activations' dynamic ranges. Furthermore, we demonstrate how to optimally allocate the bit-widths for each layer, while constraining accuracy degradation or model compression by proposing a novel integer programming formulation. Finally, we suggest model global statistics tuning, to correct biases introduced during quantization. Together, these methods yield state-of-the-art results for both vision and text models. For instance, on ResNet50, we obtain less than 1\% accuracy degradation --- with 4-bit weights and activations in all layers, but the smallest two. We open-sourced our code.

As the size of large language models (LLMs) continues to grow, model compression without sacrificing accuracy has become a crucial challenge for deployment. While some quantization methods, such as GPTQ, have made progress in achieving acceptable 4-bit weight-only quantization, attempts at lower bit quantization often result in severe performance degradation. In this paper, we introduce a technique called norm tweaking, which can be used as a plugin in current PTQ methods to achieve high precision while being cost-efficient. Our approach is inspired by the observation that rectifying the quantized activation distribution to match its float counterpart can readily restore accuracy for LLMs. To achieve this, we carefully design a tweaking strategy that includes calibration data generation and channel-wise distance constraint to update the weights of normalization layers for better generalization. We conduct extensive experiments on various datasets using several open-sourced LLMs. Our method demonstrates significant improvements in both weight-only quantization and joint quantization of weights and activations, surpassing existing PTQ methods. On GLM-130B and OPT-66B, our method even achieves the same level of accuracy at 2-bit quantization as their float ones. Our simple and effective approach makes it more practical for real-world applications.

Although post-training quantization (PTQ) provides an efficient numerical compression scheme for deploying large language models (LLMs) on resource-constrained devices, the representativeness and universality of calibration data remain a core bottleneck in determining the accuracy of quantization parameters. Traditional PTQ methods typically rely on limited samples, making it difficult to capture the activation distribution during the inference phase, leading to biases in quantization parameters. To address this, we propose FAQ (Family-Aware Quantization), a calibration data regeneration framework that leverages prior knowledge from LLMs of the same family to generate high-fidelity calibration samples. Specifically, FAQ first inputs the original calibration samples into a larger LLM from the same family as the target model, regenerating a series of high-fidelity calibration data using a highly consistent knowledge system. Subsequently, this data, carrying Chain-of-Thought reasoning and conforming to the expected activation distribution, undergoes group competition under expert guidance to select the best samples, which are then re-normalized to enhance the effectiveness of standard PTQ. Experiments on multiple model series, including Qwen3-8B, show that FAQ reduces accuracy loss by up to 28.5\% compared to the baseline with original calibration data, demonstrating its powerful potential and contribution.

The deployment of large language models (LLMs) is often constrained by memory bandwidth, where the primary bottleneck is the cost of transferring model parameters from the GPU's global memory to its registers. When coupled with custom kernels that fuse the dequantization and matmul operations, weight-only quantization can thus enable faster inference by reducing the amount of memory movement. However, developing high-performance kernels for weight-quantized LLMs presents substantial challenges, especially when the weights are compressed to non-evenly-divisible bit widths (e.g., 3 bits) with non-uniform, lookup table (LUT) quantization. This paper describes FLUTE, a flexible lookup table engine for LUT-quantized LLMs, which uses offline restructuring of the quantized weight matrix to minimize bit manipulations associated with unpacking, and vectorization and duplication of the lookup table to mitigate shared memory bandwidth constraints. At batch sizes < 32 and quantization group size of 128 (typical in LLM inference), the FLUTE kernel can be 2-4x faster than existing GEMM kernels. As an application of FLUTE, we explore a simple extension to lookup table-based NormalFloat quantization and apply it to quantize LLaMA3 to various configurations, obtaining competitive quantization performance against strong baselines while obtaining an end-to-end throughput increase of 1.5 to 2 times.

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.

Post-training quantization (PTQ) is crucial for deploying efficient object detection models, like YOLO, on resource-constrained devices. However, the impact of reduced precision on model robustness to real-world input degradations such as noise, blur, and compression artifacts is a significant concern. This paper presents a comprehensive empirical study evaluating the robustness of YOLO models (nano to extra-large scales) across multiple precision formats: FP32, FP16 (TensorRT), Dynamic UINT8 (ONNX), and Static INT8 (TensorRT). We introduce and evaluate a degradation-aware calibration strategy for Static INT8 PTQ, where the TensorRT calibration process is exposed to a mix of clean and synthetically degraded images. Models were benchmarked on the COCO dataset under seven distinct degradation conditions (including various types and levels of noise, blur, low contrast, and JPEG compression) and a mixed-degradation scenario. Results indicate that while Static INT8 TensorRT engines offer substantial speedups (~1.5-3.3x) with a moderate accuracy drop (~3-7% mAP50-95) on clean data, the proposed degradation-aware calibration did not yield consistent, broad improvements in robustness over standard clean-data calibration across most models and degradations. A notable exception was observed for larger model scales under specific noise conditions, suggesting model capacity may influence the efficacy of this calibration approach. These findings highlight the challenges in enhancing PTQ robustness and provide insights for deploying quantized detectors in uncontrolled environments. All code and evaluation tables are available at https://github.com/AllanK24/QRID.

As Large Language Models (LLMs) become increasingly computationally complex, developing efficient deployment strategies, such as quantization, becomes crucial. State-of-the-art Post-training Quantization (PTQ) techniques often rely on calibration processes to maintain the accuracy of these models. However, while these calibration techniques can enhance performance in certain domains, they may not be as effective in others. This paper aims to draw attention to robust statistical approaches that can mitigate such issues. We propose a weight-adaptive PTQ method that can be considered a precursor to calibration-based PTQ methods, guiding the quantization process to preserve the distribution of weights by minimizing the Kullback-Leibler divergence between the quantized weights and the originally trained weights. This minimization ensures that the quantized model retains the Shannon information content of the original model to a great extent, guaranteeing robust and efficient deployment across many tasks. As such, our proposed approach can perform on par with most common calibration-based PTQ methods, establishing a new pre-calibration step for further adjusting the quantized weights with calibration. We show that our pre-calibration results achieve the same accuracy as some existing calibration-based PTQ methods on various LLMs.

Quantization is a key technique to reduce network size and computational complexity by representing the network parameters with a lower precision. Traditional quantization methods rely on access to original training data, which is often restricted due to privacy concerns or security challenges. Zero-shot Quantization (ZSQ) addresses this by using synthetic data generated from pre-trained models, eliminating the need for real training data. Recently, ZSQ has been extended to object detection. However, existing methods use unlabeled task-agnostic synthetic images that lack the specific information required for object detection, leading to suboptimal performance. In this paper, we propose a novel task-specific ZSQ framework for object detection networks, which consists of two main stages. First, we introduce a bounding box and category sampling strategy to synthesize a task-specific calibration set from the pre-trained network, reconstructing object locations, sizes, and category distributions without any prior knowledge. Second, we integrate task-specific training into the knowledge distillation process to restore the performance of quantized detection networks. Extensive experiments conducted on the MS-COCO and Pascal VOC datasets demonstrate the efficiency and state-of-the-art performance of our method. Our code is publicly available at: https://github.com/DFQ-Dojo/dfq-toolkit .

Post-Training Quantization (PTQ) has received significant attention because it requires only a small set of calibration data to quantize a full-precision model, which is more practical in real-world applications in which full access to a large training set is not available. However, it often leads to overfitting on the small calibration dataset. Several methods have been proposed to address this issue, yet they still rely on only the calibration set for the quantization and they do not validate the quantized model due to the lack of a validation set. In this work, we propose a novel meta-learning based approach to enhance the performance of post-training quantization. Specifically, to mitigate the overfitting problem, instead of only training the quantized model using the original calibration set without any validation during the learning process as in previous PTQ works, in our approach, we both train and validate the quantized model using two different sets of images. In particular, we propose a meta-learning based approach to jointly optimize a transformation network and a quantized model through bi-level optimization. The transformation network modifies the original calibration data and the modified data will be used as the training set to learn the quantized model with the objective that the quantized model achieves a good performance on the original calibration data. Extensive experiments on the widely used ImageNet dataset with different neural network architectures demonstrate that our approach outperforms the state-of-the-art PTQ methods.

Large Language Models (LLMs) are proficient in natural language processing tasks, but their deployment is often restricted by extensive parameter sizes and computational demands. This paper focuses on post-training quantization (PTQ) in LLMs, specifically 4-bit weight and 8-bit activation (W4A8) quantization, to enhance computational efficiency -- a topic less explored compared to weight-only quantization. We present two innovative techniques: activation-quantization-aware scaling (AQAS) and sequence-length-aware calibration (SLAC) to enhance PTQ by considering the combined effects on weights and activations and aligning calibration sequence lengths to target tasks. Moreover, we introduce dINT, a hybrid data format combining integer and denormal representations, to address the underflow issue in W4A8 quantization, where small values are rounded to zero. Through rigorous evaluations of LLMs, including OPT and LLaMA, we demonstrate that our techniques significantly boost task accuracies to levels comparable with full-precision models. By developing arithmetic units compatible with dINT, we further confirm that our methods yield a 2times hardware efficiency improvement compared to 8-bit integer MAC unit.

Post-training quantization has emerged as the most widely used strategy for deploying large language models at low precision. Still, current methods show perplexity degradation at bit-widths less than or equal to 4, partly because representing outliers causes precision issues in parameters that share the same scales as these outliers. This problem is especially pronounced for calibration-free, uniform quantization methods. We introduce SINQ to augment existing post-training quantizers with an additional second-axis scale factor and a fast Sinkhorn-Knopp-style algorithm that finds scales to normalize per-row and per-column variances, thereby minimizing a novel per-matrix proxy target for quantization: the matrix imbalance. Our method has no interactions between layers and can be trivially applied to new architectures to quantize any linear layers. We evaluate our method on the Qwen3 model family and DeepSeek-V2.5. SINQ improves WikiText2 and C4 perplexity significantly against uncalibrated uniform quantization baselines and can be further enhanced by combining it with calibration and non-uniform quantization levels. Code to reproduce the results of this work and to easily quantize models using SINQ is available at https://github.com/huawei-csl/SINQ.

Model quantification uses low bit-width values to represent the weight matrices of models, which is a promising approach to reduce both storage and computational overheads of deploying highly anticipated LLMs. However, existing quantization methods suffer severe performance degradation when the bit-width is extremely reduced, and thus focus on utilizing 4-bit or 8-bit values to quantize models. This paper boldly quantizes the weight matrices of LLMs to 1-bit, paving the way for the extremely low bit-width deployment of LLMs. For this target, we introduce a 1-bit quantization-aware training (QAT) framework named OneBit, including a novel 1-bit parameter representation method to better quantize LLMs as well as an effective parameter initialization method based on matrix decomposition to improve the convergence speed of the QAT framework. Sufficient experimental results indicate that OneBit achieves good performance (at least 83% of the non-quantized performance) with robust training processes when only using 1-bit weight matrices.

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.

Post-Training Quantization (PTQ) enhances the efficiency of Large Language Models (LLMs) by enabling faster operation and compatibility with more accessible hardware through reduced memory usage, at the cost of small performance drops. We explore the role of calibration sets in PTQ, specifically their effect on hidden activations in various notable open-source LLMs. Calibration sets are crucial for evaluating activation magnitudes and identifying outliers, which can distort the quantization range and negatively impact performance. Our analysis reveals a marked contrast in quantization effectiveness across models. The older OPT model, upon which much of the quantization literature is based, shows significant performance deterioration and high susceptibility to outliers with varying calibration sets. In contrast, newer models like Llama-2 7B, Llama-3 8B, Command-R 35B, and Mistral 7B demonstrate strong robustness, with Mistral 7B showing near-immunity to outliers and stable activations. These findings suggest a shift in PTQ strategies might be needed. As advancements in pre-training methods reduce the relevance of outliers, there is an emerging need to reassess the fundamentals of current quantization literature. The emphasis should pivot towards optimizing inference speed, rather than primarily focusing on outlier preservation, to align with the evolving characteristics of state-of-the-art LLMs.

Recent studies introduced effective compression techniques for Large Language Models (LLMs) via post-training quantization or low-bit weight representation. Although quantized weights offer storage efficiency and allow for faster inference, existing works have indicated that quantization might compromise performance and exacerbate biases in LLMs. This study investigates the confidence and calibration of quantized models, considering factors such as language model type and scale as contributors to quantization loss. Firstly, we reveal that quantization with GPTQ to 4-bit results in a decrease in confidence regarding true labels, with varying impacts observed among different language models. Secondly, we observe fluctuations in the impact on confidence across different scales. Finally, we propose an explanation for quantization loss based on confidence levels, indicating that quantization disproportionately affects samples where the full model exhibited low confidence levels in the first place.

Post-training quantization (PTQ) is a primary approach for deploying large language models without fine-tuning, and the quantized performance is often strongly affected by the calibration in PTQ. By contrast, in vision-language models (VLMs), substantial differences between visual and text tokens in their activation distributions and sensitivities to quantization error pose significant challenges for effective calibration during PTQ. In this work, we rethink what PTQ calibration should align with in VLMs and propose the Token-level Importance-aware Layer-wise Quantization framework (TLQ). Guided by gradient information, we design a token-level importance integration mechanism for quantization error, and use it to construct a token-level calibration set, enabling a more fine-grained calibration strategy. Furthermore, TLQ introduces a multi-GPU, quantization-exposed layer-wise calibration scheme. This scheme keeps the layer-wise calibration procedure consistent with the true quantized inference path and distributes the complex layer-wise calibration workload across multiple RTX3090 GPUs, thereby reducing reliance on the large memory of A100 GPUs. TLQ is evaluated across two models, three model scales, and two quantization settings, consistently achieving performance improvements across all settings, indicating its strong quantization stability. The code will be released publicly.

Large Language Models (LLMs) have shown an impressive capability in code generation and, specifically, to automatically implement requirements described in natural language. The LLM effectiveness generally increases with its size: The higher the number of LLM's trainable parameters the better its ability to implement code. However, when it comes to deploying LLM-based code generators, larger LLMs pose significant challenges related to their memory (and, consequently, carbon) footprint. A previous work by Wei et al. proposed to leverage quantization techniques to reduce the memory footprint of LLM-based code generators without substantially degrading their effectiveness. In short, they studied LLMs featuring up to 16B parameters, quantizing their precision from floating point 32 bits down to int 8 bits and showing their limited impact on code generation performance. Given the fast pace at which LLM capabilities and quantization techniques are evolving, in this work we present a differentiated replication of the work by Wei et al. in which we consider (i) on the one side, more recent and larger code-related LLMs, of up to 34B parameters; (ii) the latest advancements in model quantization techniques, which allow pushing the compression to the extreme quantization level of 2 bits per model parameter and; (iii) different types of calibration datasets to guide the quantization process, including code-specific ones. Our empirical evaluation reveals that the new frontier for LLM quantization is 4-bit precision, resulting in an average memory footprint reduction of 70% compared to the original model without observing any significant decrease in performance. Additionally, when the quantization becomes even more extreme (3 and 2 bits), a code-specific calibration dataset helps to limit the loss of performance.

A lot of recent progress has been made in ultra low-bit quantization, promising significant improvements in latency, memory footprint and energy consumption on edge devices. Quantization methods such as Learned Step Size Quantization can achieve model accuracy that is comparable to full-precision floating-point baselines even with sub-byte quantization. However, it is extremely challenging to deploy these ultra low-bit quantized models on mainstream CPU devices because commodity SIMD (Single Instruction, Multiple Data) hardware typically supports no less than 8-bit precision. To overcome this limitation, we propose DeepGEMM, a lookup table based approach for the execution of ultra low-precision convolutional neural networks on SIMD hardware. The proposed method precomputes all possible products of weights and activations, stores them in a lookup table, and efficiently accesses them at inference time to avoid costly multiply-accumulate operations. Our 2-bit implementation outperforms corresponding 8-bit integer kernels in the QNNPACK framework by up to 1.74x on x86 platforms.

Pruning and quantization form the foundation of model compression for neural networks, enabling efficient inference for large language models (LLMs). Recently, various quantization and pruning techniques have demonstrated state-of-the-art performance in a post-training setting. They rely upon calibration data, a small set of unlabeled examples, to generate layer activations. However, no prior work has systematically investigated how the calibration data impacts the effectiveness of model compression methods. In this paper, we present the first extensive empirical study on the effect of calibration data upon LLM performance. We trial a variety of pruning and quantization methods, tasks, models, and datasets. Surprisingly, we find substantial variations in downstream task performance, contrasting existing work that suggests a greater level of robustness to the calibration data. Finally, we make a series of recommendations for the effective use of calibration data in LLM quantization and pruning.

Post-training model compression is essential for enhancing the portability of Large Language Models (LLMs) while preserving their performance. While several compression approaches have been proposed, less emphasis has been placed on selecting the most suitable set of data (the so-called calibration data) for finding the compressed model configuration. The choice of calibration data is a critical step in preserving model capabilities both intra- and inter-tasks. In this work, we address the challenge of identifying high-performance calibration sets for both pruning and quantization by analyzing intrinsic data properties rather than model-specific signals. We introduce \textbf{ZipCal}, a model-agnostic data curation strategy that maximizes lexical diversity based on Zipfian power laws. Experiments demonstrate that our method consistently outperforms standard uniform random sampling across various pruning benchmarks. Notably, it also performs on par, in terms of downstream performance, with a state-of-the-art method that relies on model perplexity. The latter becomes prohibitively expensive at large-scale models and datasets, while \textbf{ZipCal} is on average sim240times faster due to its tractable linear complexityWe make the code and the experiments available at https://anonymous.4open.science/r/zipcal-71CD/..

Post-training quantization (PTQ) is a cornerstone for efficiently deploying large language models (LLMs), where a small calibration set critically affects quantization performance. However, conventional practices rely on random sequences of fixed length, overlooking the variable-length nature of LLM inputs. Input length directly influences the activation distribution and, consequently, the weight importance captured by the Hessian, which in turn affects quantization outcomes. As a result, Hessian estimates derived from fixed-length calibration may fail to represent the true importance of weights across diverse input scenarios. We propose MaCa (Matryoshka Calibration), a simple yet effective method for length-aware Hessian construction. MaCa (i) incorporates multi-scale sequence length information into Hessian estimation and (ii) regularizes each sequence as an independent sample, yielding a more stable and fruitful Hessian for accurate quantization. Experiments on state-of-the-art LLMs (e.g., Qwen3, Gemma3, LLaMA3) demonstrate that MaCa consistently improves accuracy under low bit quantization, offering a lightweight enhancement compatible with existing PTQ frameworks. To the best of our knowledge, this is the first work to systematically highlight the role of multi-scale calibration in LLM quantization.

Recent advancements in large language models (LLMs) are propelling us toward artificial general intelligence with their remarkable emergent abilities and reasoning capabilities. However, the substantial computational and memory requirements limit the widespread adoption. Quantization, a key compression technique, can effectively mitigate these demands by compressing and accelerating LLMs, albeit with potential risks to accuracy. Numerous studies have aimed to minimize the accuracy loss associated with quantization. However, their quantization configurations vary from each other and cannot be fairly compared. In this paper, we present LLMC, a plug-and-play compression toolkit, to fairly and systematically explore the impact of quantization. LLMC integrates dozens of algorithms, models, and hardwares, offering high extensibility from integer to floating-point quantization, from LLM to vision-language (VLM) model, from fixed-bit to mixed precision, and from quantization to sparsification. Powered by this versatile toolkit, our benchmark covers three key aspects: calibration data, algorithms (three strategies), and data formats, providing novel insights and detailed analyses for further research and practical guidance for users. Our toolkit is available at https://github.com/ModelTC/llmc.

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}.

Methods based on weight compensation, which iteratively apply quantization and weight compensation to minimize the output error, have recently demonstrated remarkable success in quantizing Large Language Models (LLMs). The representative work, GPTQ, introduces several key techniques that make such iterative methods practical for LLMs with billions of parameters. GPTAQ extends this approach by introducing an asymmetric calibration process that aligns the output of each quantized layer with its full-precision counterpart, incorporating a residual error into the weight compensation framework. In this work, we revisit the formulation of the residual error. We identify a sub-optimal calibration objective in existing methods: during the intra-layer calibration process, they align the quantized output with the output from compensated weights, rather than the true output from the original full-precision model. Therefore, we redefine the objective to precisely align the quantized model's output with the original output of the full-precision model at each step. We then reveal that the residual error originates not only from the output difference of the preceding layer but also from the discrepancy between the compensated and original weights within each layer, which we name the 'compensation-aware error'. By inheriting the neuron decomposition technique from GPTAQ, we can efficiently incorporate this compensation-aware error into the weight update process. Extensive experiments on various LLMs and quantization settings demonstrate that our proposed enhancements integrate seamlessly with both GPTQ and GPTAQ, significantly improving their quantization performance. Our code is publicly available at https://github.com/list0830/ResComp.

Quantization Aware Training (QAT) is a neural network quantization technique that compresses model size and improves operational efficiency while effectively maintaining model performance. The paradigm of QAT is to introduce fake quantization operators during the training process, allowing the model to autonomously compensate for information loss caused by quantization. Making quantization parameters trainable can significantly improve the performance of QAT, but at the cost of compromising the flexibility during inference, especially when dealing with activation values with substantially different distributions. In this paper, we propose an effective learnable adaptive neural network quantization method, called Adaptive Step Size Quantization (ASQ), to resolve this conflict. Specifically, the proposed ASQ method first dynamically adjusts quantization scaling factors through a trained module capable of accommodating different activations. Then, to address the rigid resolution issue inherent in Power of Two (POT) quantization, we propose an efficient non-uniform quantization scheme. We utilize the Power Of Square root of Two (POST) as the basis for exponential quantization, effectively handling the bell-shaped distribution of neural network weights across various bit-widths while maintaining computational efficiency through a Look-Up Table method (LUT). Extensive experimental results demonstrate that the proposed ASQ method is superior to the state-of-the-art QAT approaches. Notably that the ASQ is even competitive compared to full precision baselines, with its 4-bit quantized ResNet34 model improving accuracy by 1.2\% on ImageNet.

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.

Recent advancements in machine learning achieved by Deep Neural Networks (DNNs) have been significant. While demonstrating high accuracy, DNNs are associated with a huge number of parameters and computations, which leads to high memory usage and energy consumption. As a result, deploying DNNs on devices with constrained hardware resources poses significant challenges. To overcome this, various compression techniques have been widely employed to optimize DNN accelerators. A promising approach is quantization, in which the full-precision values are stored in low bit-width precision. Quantization not only reduces memory requirements but also replaces high-cost operations with low-cost ones. DNN quantization offers flexibility and efficiency in hardware design, making it a widely adopted technique in various methods. Since quantization has been extensively utilized in previous works, there is a need for an integrated report that provides an understanding, analysis, and comparison of different quantization approaches. Consequently, we present a comprehensive survey of quantization concepts and methods, with a focus on image classification. We describe clustering-based quantization methods and explore the use of a scale factor parameter for approximating full-precision values. Moreover, we thoroughly review the training of a quantized DNN, including the use of a straight-through estimator and quantization regularization. We explain the replacement of floating-point operations with low-cost bitwise operations in a quantized DNN and the sensitivity of different layers in quantization. Furthermore, we highlight the evaluation metrics for quantization methods and important benchmarks in the image classification task. We also present the accuracy of the state-of-the-art methods on CIFAR-10 and ImageNet.

Network quantization generally converts full-precision weights and/or activations into low-bit fixed-point values in order to accelerate an inference process. Recent approaches to network quantization further discretize the gradients into low-bit fixed-point values, enabling an efficient training. They typically set a quantization interval using a min-max range of the gradients or adjust the interval such that the quantization error for entire gradients is minimized. In this paper, we analyze the quantization error of gradients for the low-bit fixed-point training, and show that lowering the error for large-magnitude gradients boosts the quantization performance significantly. Based on this, we derive an upper bound of quantization error for the large gradients in terms of the quantization interval, and obtain an optimal condition for the interval minimizing the quantization error for large gradients. We also introduce an interval update algorithm that adjusts the quantization interval adaptively to maintain a small quantization error for large gradients. Experimental results demonstrate the effectiveness of our quantization method for various combinations of network architectures and bit-widths on various tasks, including image classification, object detection, and super-resolution.

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.

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.

While neural networks have advanced the frontiers in many applications, they often come at a high computational cost. Reducing the power and latency of neural network inference is key if we want to integrate modern networks into edge devices with strict power and compute requirements. Neural network quantization is one of the most effective ways of achieving these savings but the additional noise it induces can lead to accuracy degradation. In this white paper, we introduce state-of-the-art algorithms for mitigating the impact of quantization noise on the network's performance while maintaining low-bit weights and activations. We start with a hardware motivated introduction to quantization and then consider two main classes of algorithms: Post-Training Quantization (PTQ) and Quantization-Aware-Training (QAT). PTQ requires no re-training or labelled data and is thus a lightweight push-button approach to quantization. In most cases, PTQ is sufficient for achieving 8-bit quantization with close to floating-point accuracy. QAT requires fine-tuning and access to labeled training data but enables lower bit quantization with competitive results. For both solutions, we provide tested pipelines based on existing literature and extensive experimentation that lead to state-of-the-art performance for common deep learning models and tasks.

Post-training quantization (PTQ) has emerged as a practical approach to compress large neural networks, making them highly efficient for deployment. However, effectively reducing these models to their low-bit counterparts without compromising the original accuracy remains a key challenge. In this paper, we propose an innovative PTQ algorithm termed COMQ, which sequentially conducts coordinate-wise minimization of the layer-wise reconstruction errors. We consider the widely used integer quantization, where every quantized weight can be decomposed into a shared floating-point scalar and an integer bit-code. Within a fixed layer, COMQ treats all the scaling factor(s) and bit-codes as the variables of the reconstruction error. Every iteration improves this error along a single coordinate while keeping all other variables constant. COMQ is easy to use and requires no hyper-parameter tuning. It instead involves only dot products and rounding operations. We update these variables in a carefully designed greedy order, significantly enhancing the accuracy. COMQ achieves remarkable results in quantizing 4-bit Vision Transformers, with a negligible loss of less than 1% in Top-1 accuracy. In 4-bit INT quantization of convolutional neural networks, COMQ maintains near-lossless accuracy with a minimal drop of merely 0.3% in Top-1 accuracy.

Quantization and cache mechanisms are typically applied individually for efficient Diffusion Transformers (DiTs), each demonstrating notable potential for acceleration. However, the promoting effect of combining the two mechanisms on efficient generation remains under-explored. Through empirical investigation, we find that the combination of quantization and cache mechanisms for DiT is not straightforward, and two key challenges lead to severe catastrophic performance degradation: (i) the sample efficacy of calibration datasets in post-training quantization (PTQ) is significantly eliminated by cache operation; (ii) the combination of the above mechanisms introduces more severe exposure bias within sampling distribution, resulting in amplified error accumulation in the image generation process. In this work, we take advantage of these two acceleration mechanisms and propose a hybrid acceleration method by tackling the above challenges, aiming to further improve the efficiency of DiTs while maintaining excellent generation capability. Concretely, a temporal-aware parallel clustering (TAP) is designed to dynamically improve the sample selection efficacy for the calibration within PTQ for different diffusion steps. A variance compensation (VC) strategy is derived to correct the sampling distribution. It mitigates exposure bias through an adaptive correction factor generation. Extensive experiments have shown that our method has accelerated DiTs by 12.7x while preserving competitive generation capability. The code will be available at https://github.com/xinding-sys/Quant-Cache.

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.

Video matting is crucial for applications such as film production and virtual reality, yet deploying its computationally intensive models on resource-constrained devices presents challenges. Quantization is a key technique for model compression and acceleration. As an efficient approach, Post-Training Quantization (PTQ) is still in its nascent stages for video matting, facing significant hurdles in maintaining accuracy and temporal coherence. To address these challenges, this paper proposes a novel and general PTQ framework specifically designed for video matting models, marking, to the best of our knowledge, the first systematic attempt in this domain. Our contributions include: (1) A two-stage PTQ strategy that combines block-reconstruction-based optimization for fast, stable initial quantization and local dependency capture, followed by a global calibration of quantization parameters to minimize accuracy loss. (2) A Statistically-Driven Global Affine Calibration (GAC) method that enables the network to compensate for cumulative statistical distortions arising from factors such as neglected BN layer effects, even reducing the error of existing PTQ methods on video matting tasks up to 20%. (3) An Optical Flow Assistance (OFA) component that leverages temporal and semantic priors from frames to guide the PTQ process, enhancing the model's ability to distinguish moving foregrounds in complex scenes and ultimately achieving near full-precision performance even under ultra-low-bit quantization. Comprehensive quantitative and visual results show that our PTQ4VM achieves the state-of-the-art accuracy performance across different bit-widths compared to the existing quantization methods. We highlight that the 4-bit PTQ4VM even achieves performance close to the full-precision counterpart while enjoying 8x FLOP savings.

We introduce GPTQv2, a novel finetuning-free quantization method for compressing large-scale transformer architectures. Unlike the previous GPTQ method, which independently calibrates each layer, we always match the quantized layer's output to the exact output in the full-precision model, resulting in a scheme that we call asymmetric calibration. Such a scheme can effectively reduce the quantization error accumulated in previous layers. We analyze this problem using optimal brain compression to derive a close-formed solution. The new solution explicitly minimizes the quantization error as well as the accumulated asymmetry error. Furthermore, we utilize various techniques to parallelize the solution calculation, including channel parallelization, neuron decomposition, and Cholesky reformulation for matrix fusion. As a result, GPTQv2 is easy to implement, simply using 20 more lines of code than GPTQ but improving its performance under low-bit quantization. Remarkably, on a single GPU, we quantize a 405B language transformer as well as EVA-02 the rank first vision transformer that achieves 90% pretraining Imagenet accuracy. Code is available at github.com/Intelligent-Computing-Lab-Yale/GPTQv2.

Large Language Model (LLM) inference is typically memory-intensive, especially when processing large batch sizes and long sequences, due to the large size of key-value (KV) cache. Vector Quantization (VQ) is recently adopted to alleviate this issue, but we find that the existing approach is susceptible to distribution shift due to its reliance on calibration datasets. To address this limitation, we introduce NSNQuant, a calibration-free Vector Quantization (VQ) technique designed for low-bit compression of the KV cache. By applying a three-step transformation-1) a token-wise normalization (Normalize), 2) a channel-wise centering (Shift), and 3) a second token-wise normalization (Normalize)-with Hadamard transform, NSNQuant effectively aligns the token distribution with the standard normal distribution. This alignment enables robust, calibration-free vector quantization using a single reusable codebook. Extensive experiments show that NSNQuant consistently outperforms prior methods in both 1-bit and 2-bit settings, offering strong generalization and up to 3times throughput gain over full-precision baselines.

Model quantization reduces neural network parameter precision to achieve compression, but often compromises accuracy. Existing post-training quantization (PTQ) methods employ iterative parameter updates to preserve accuracy under high compression ratios, incurring significant computational complexity and resource overhead, which limits applicability in resource-constrained edge computing and real-time inference scenarios. This paper proposes an efficient PTQ method guided by parameter sensitivity analysis. The approach prioritizes quantization of high-sensitivity parameters, leveraging unquantized low-sensitivity parameters to compensate for quantization errors, thereby mitigating accuracy degradation. Furthermore, by exploiting column-wise clustering of parameter sensitivity, the method introduces a row-parallel quantization framework with a globally shared inverse Hessian matrix update mechanism, reducing computational complexity by an order of magnitude. Experimental results on ResNet-50 and YOLOv5s demonstrate a 20-200-fold quantization speedup over the Optimal Brain Quantization baseline, with mean accuracy loss below 0.3%, confirming the method's efficacy in balancing efficiency and accuracy.

Diffusion models have achieved great success in image generation tasks through iterative noise estimation. However, the heavy denoising process and complex neural networks hinder their low-latency applications in real-world scenarios. Quantization can effectively reduce model complexity, and post-training quantization (PTQ), which does not require fine-tuning, is highly promising in accelerating the denoising process. Unfortunately, we find that due to the highly dynamic distribution of activations in different denoising steps, existing PTQ methods for diffusion models suffer from distribution mismatch issues at both calibration sample level and reconstruction output level, which makes the performance far from satisfactory, especially in low-bit cases. In this paper, we propose Enhanced Distribution Alignment for Post-Training Quantization of Diffusion Models (EDA-DM) to address the above issues. Specifically, at the calibration sample level, we select calibration samples based on the density and diversity in the latent space, thus facilitating the alignment of their distribution with the overall samples; and at the reconstruction output level, we propose Fine-grained Block Reconstruction, which can align the outputs of the quantized model and the full-precision model at different network granularity. Extensive experiments demonstrate that EDA-DM outperforms the existing post-training quantization frameworks in both unconditional and conditional generation scenarios. At low-bit precision, the quantized models with our method even outperform the full-precision models on most datasets.

This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from incoherent weight and Hessian matrices, i.e., from the weights and the directions in which it is important to round them accurately being unaligned with the coordinate axes. QuIP consists of two steps: (1) an adaptive rounding procedure minimizing a quadratic proxy objective; (2) efficient pre- and post-processing that ensures weight and Hessian incoherence via multiplication by random orthogonal matrices. We complement QuIP with the first theoretical analysis for an LLM-scale quantization algorithm, and show that our theory also applies to an existing method, OPTQ. Empirically, we find that our incoherence preprocessing improves several existing quantization algorithms and yields the first LLM quantization methods that produce viable results using only two bits per weight. Our code can be found at https://github.com/jerry-chee/QuIP .

Post-training quantization (PTQ) offers an efficient approach to compressing large language models (LLMs), significantly reducing memory access and computational costs. Existing compensation-based weight calibration methods often rely on a second-order Taylor expansion to model quantization error, under the assumption that the first-order term is negligible in well-trained full-precision models. However, we reveal that the progressive compensation process introduces accumulated first-order deviations between latent weights and their full-precision counterparts, making this assumption fundamentally flawed. To address this, we propose FOEM, a novel PTQ method that explicitly incorporates first-order gradient terms to improve quantization error compensation. FOEM approximates gradients by performing a first-order Taylor expansion around the pre-quantization weights. This yields an approximation based on the difference between latent and full-precision weights as well as the Hessian matrix. When substituted into the theoretical solution, the formulation eliminates the need to explicitly compute the Hessian, thereby avoiding the high computational cost and limited generalization of backpropagation-based gradient methods. This design introduces only minimal additional computational overhead. Extensive experiments across a wide range of models and benchmarks demonstrate that FOEM consistently outperforms the classical GPTQ method. In 3-bit weight-only quantization, FOEM reduces the perplexity of Llama3-8B by 17.3% and increases the 5-shot MMLU accuracy from 53.8% achieved by GPTAQ to 56.1%. Moreover, FOEM can be seamlessly combined with advanced techniques such as SpinQuant, delivering additional gains under the challenging W4A4KV4 setting and further narrowing the performance gap with full-precision baselines, surpassing existing state-of-the-art methods.

Large language model (LLM) inference is often bounded by memory footprint and memory bandwidth in resource-constrained deployments, making quantization a fundamental technique for efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. Fundamentally, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using approximate second-order information while progressively compensating quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we provide theoretical analysis showing that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. Code: github.com/KingdalfGoodman/BPDQ.

Quantized neural networks can be viewed as a chain of noisy channels, where rounding in each layer reduces capacity as bit-width shrinks; the floating-point (FP) checkpoint sets the maximum input rate. We track capacity dynamics as the average bit-width decreases and identify resulting quantization bottlenecks by casting fine-tuning as a smooth, constrained optimization problem. Our approach employs a fully differentiable Straight-Through Estimator (STE) with learnable bit-width, noise scale and clamp bounds, and enforces a target bit-width via an exterior-point penalty; mild metric smoothing (via distillation) stabilizes training. Despite its simplicity, the method attains competitive accuracy down to the extreme W1A1 setting while retaining the efficiency of STE.

We present an overview of techniques for quantizing convolutional neural networks for inference with integer weights and activations. Per-channel quantization of weights and per-layer quantization of activations to 8-bits of precision post-training produces classification accuracies within 2% of floating point networks for a wide variety of CNN architectures. Model sizes can be reduced by a factor of 4 by quantizing weights to 8-bits, even when 8-bit arithmetic is not supported. This can be achieved with simple, post training quantization of weights.We benchmark latencies of quantized networks on CPUs and DSPs and observe a speedup of 2x-3x for quantized implementations compared to floating point on CPUs. Speedups of up to 10x are observed on specialized processors with fixed point SIMD capabilities, like the Qualcomm QDSPs with HVX. Quantization-aware training can provide further improvements, reducing the gap to floating point to 1% at 8-bit precision. Quantization-aware training also allows for reducing the precision of weights to four bits with accuracy losses ranging from 2% to 10%, with higher accuracy drop for smaller networks.We introduce tools in TensorFlow and TensorFlowLite for quantizing convolutional networks and review best practices for quantization-aware training to obtain high accuracy with quantized weights and activations. We recommend that per-channel quantization of weights and per-layer quantization of activations be the preferred quantization scheme for hardware acceleration and kernel optimization. We also propose that future processors and hardware accelerators for optimized inference support precisions of 4, 8 and 16 bits.

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

Serving large-scale machine learning (ML) models efficiently and with low latency has become challenging owing to increasing model size and complexity. Quantizing models can simultaneously reduce memory and compute requirements, facilitating their widespread access. However, for large models not all layers are equally amenable to the same numerical precision and aggressive quantization can lead to unacceptable loss in model accuracy. One approach to prevent this accuracy degradation is mixed-precision quantization, which allows different tensors to be quantized to varying levels of numerical precision, leveraging the capabilities of modern hardware. Such mixed-precision quantiztaion can more effectively allocate numerical precision to different tensors `as needed' to preserve model accuracy while reducing footprint and compute latency. In this paper, we propose a method to efficiently determine quantization configurations of different tensors in ML models using post-training mixed precision quantization. We analyze three sensitivity metrics and evaluate them for guiding configuration search of two algorithms. We evaluate our method for computer vision and natural language processing and demonstrate latency reductions of up to 27.59% and 34.31% compared to the baseline 16-bit floating point model while guaranteeing no more than 1% accuracy degradation.

Quantization has become a mainstream compression technique for reducing model size, computational requirements, and energy consumption for modern deep neural networks (DNNs). With the improved numerical support in recent hardware, including multiple variants of integer and floating point, mixed-precision quantization has become necessary to achieve high-quality results with low model cost. Prior mixed-precision quantization methods have performed a post-training quantization search, which compromises on accuracy, or a differentiable quantization search, which leads to high memory usage from branching. Therefore, we propose the first one-shot mixed-precision quantization search that eliminates the need for retraining in both integer and low-precision floating point models. We evaluate our floating-point and integer quantization search (FLIQS) on multiple convolutional networks and vision transformer models to discover Pareto-optimal models. Our approach discovers models that improve upon uniform precision, manual mixed-precision, and recent integer quantization search methods. With the proposed integer quantization search, we increase the accuracy of ResNet-18 on ImageNet by 1.31% points and ResNet-50 by 0.90% points with equivalent model cost over previous methods. Additionally, for the first time, we explore a novel mixed-precision floating-point search and improve MobileNetV2 by up to 0.98% points compared to prior state-of-the-art FP8 models. Finally, we extend FLIQS to simultaneously search a joint quantization and neural architecture space and improve the ImageNet accuracy by 2.69% points with similar model cost on a MobileNetV2 search space.

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.

Post-training quantization (PTQ), which only requires a tiny dataset for calibration without end-to-end retraining, is a light and practical model compression technique. Recently, several PTQ schemes for vision transformers (ViTs) have been presented; unfortunately, they typically suffer from non-trivial accuracy degradation, especially in low-bit cases. In this paper, we propose RepQ-ViT, a novel PTQ framework for ViTs based on quantization scale reparameterization, to address the above issues. RepQ-ViT decouples the quantization and inference processes, where the former employs complex quantizers and the latter employs scale-reparameterized simplified quantizers. This ensures both accurate quantization and efficient inference, which distinguishes it from existing approaches that sacrifice quantization performance to meet the target hardware. More specifically, we focus on two components with extreme distributions: post-LayerNorm activations with severe inter-channel variation and post-Softmax activations with power-law features, and initially apply channel-wise quantization and log2 quantization, respectively. Then, we reparameterize the scales to hardware-friendly layer-wise quantization and log2 quantization for inference, with only slight accuracy or computational costs. Extensive experiments are conducted on multiple vision tasks with different model variants, proving that RepQ-ViT, without hyperparameters and expensive reconstruction procedures, can outperform existing strong baselines and encouragingly improve the accuracy of 4-bit PTQ of ViTs to a usable level. Code is available at https://github.com/zkkli/RepQ-ViT.

There has been significant interest in "extreme" compression of large language models (LLMs), i.e., to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs. We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases. On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama 2 family models at 2 bits per parameter.

The diffusion model has gained popularity in vision applications due to its remarkable generative performance and versatility. However, high storage and computation demands, resulting from the model size and iterative generation, hinder its use on mobile devices. Existing quantization techniques struggle to maintain performance even in 8-bit precision due to the diffusion model's unique property of temporal variation in activation. We introduce a novel quantization method that dynamically adjusts the quantization interval based on time step information, significantly improving output quality. Unlike conventional dynamic quantization techniques, our approach has no computational overhead during inference and is compatible with both post-training quantization (PTQ) and quantization-aware training (QAT). Our extensive experiments demonstrate substantial improvements in output quality with the quantized diffusion model across various datasets.

Diffusion Transformers (DiTs) have recently gained substantial attention in both industrial and academic fields for their superior visual generation capabilities, outperforming traditional diffusion models that use U-Net. However,the enhanced performance of DiTs also comes with high parameter counts and implementation costs, seriously restricting their use on resource-limited devices such as mobile phones. To address these challenges, we introduce the Hybrid Floating-point Quantization for DiT(HQ-DiT), an efficient post-training quantization method that utilizes 4-bit floating-point (FP) precision on both weights and activations for DiT inference. Compared to fixed-point quantization (e.g., INT8), FP quantization, complemented by our proposed clipping range selection mechanism, naturally aligns with the data distribution within DiT, resulting in a minimal quantization error. Furthermore, HQ-DiT also implements a universal identity mathematical transform to mitigate the serious quantization error caused by the outliers. The experimental results demonstrate that DiT can achieve extremely low-precision quantization (i.e., 4 bits) with negligible impact on performance. Our approach marks the first instance where both weights and activations in DiTs are quantized to just 4 bits, with only a 0.12 increase in sFID on ImageNet.

Deep neural networks have achieved state-of-the-art results in a wide range of applications, from natural language processing and computer vision to speech recognition. However, as tasks become increasingly complex, model sizes continue to grow, posing challenges in latency and memory efficiency. To meet these constraints, post-training quantization has emerged as a promising solution. In this paper, we propose a novel hardware-efficient quantization and inference scheme that exploits hardware advantages with minimal accuracy degradation. Specifically, we introduce a W4A8 scheme, where weights are quantized and stored using 4-bit integer precision, and inference computations are performed using 8-bit floating-point arithmetic, demonstrating significant speedups and improved memory utilization compared to 16-bit operations, applicable on various modern accelerators. To mitigate accuracy loss, we develop a novel quantization algorithm, dubbed Dual Precision Quantization (DPQ), that leverages the unique structure of our scheme without introducing additional inference overhead. Experimental results demonstrate improved performance (i.e., increased throughput) while maintaining tolerable accuracy degradation relative to the full-precision model.

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.

Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.

Straight-through estimator (STE), which enables the gradient flow over the non-differentiable function via approximation, has been favored in studies related to quantization-aware training (QAT). However, STE incurs unstable convergence during QAT, resulting in notable quality degradation in low precision. Recently, pseudoquantization training has been proposed as an alternative approach to updating the learnable parameters using the pseudo-quantization noise instead of STE. In this study, we propose a novel noise proxy-based integrated pseudoquantization (NIPQ) that enables unified support of pseudoquantization for both activation and weight by integrating the idea of truncation on the pseudo-quantization framework. NIPQ updates all of the quantization parameters (e.g., bit-width and truncation boundary) as well as the network parameters via gradient descent without STE instability. According to our extensive experiments, NIPQ outperforms existing quantization algorithms in various vision and language applications by a large margin.

This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical evaluation across models ranging from 10M to 1B parameters, we demonstrate that quantization can achieve up to 68% reduction in model size while maintaining performance within 6% of full-precision baselines when utilizing our proposed scaling factor {\gamma}. Our experiments show that INT8 quantization delivers a 40% reduction in computational cost and power consumption, while INT4 quantization further improves these metrics by 60%. We introduce a novel theoretical framework for mixed-precision quantization, deriving optimal bit allocation strategies based on layer sensitivity and weight variance. Hardware efficiency evaluations on edge devices reveal that our quantization approach enables up to 2.4x throughput improvement for INT8 and 3x for INT4, with 60% power reduction compared to full-precision models.

Recent years have witnessed an increasing interest in deploying LLMs on resource-constrained devices, among which quantization has emerged as a promising lightweight technique that converts full-precision model weights and activations into lower-bit formats. Existing weight quantization approaches can be roughly divided into three categories: Post-Training Quantization (PTQ) that calibrates quantized parameters on a small dataset without retraining but suffers from severe performance degradation below 4-bit, Quantization-Aware Training (QAT) that searches low-bit parameters using surrogate gradients but demands substantial computational resources, and Quantization-Aware Distillation that integrates QAT with knowledge transfer from a full-precision teacher but manually selects features to distill and relies heavily on teacher-specific data. In this paper, we propose EdgeRazor, a lightweight framework for LLMs with mixed-precision and extremely low-bit weight quantization. The EdgeRazor framework contains three modules: Mixed-Precision Quantization-Aware Distillation for the fine-grained control of precision, Adaptive Feature Distillation that derives an n-bit student from its 16-bit teacher, and Entropy-Aware KL Divergence on both human-annotated and distilled datasets, whose forward-reverse balance is determined solely by the teacher's output distribution. Empirical investigations of EdgeRazor are conducted on base, instruction-tuned, and multimodal LLMs. Notably, EdgeRazor with 1.88-bit surpasses all contenders with the 3-bit precision, especially outperforms the leading 2-bit PTQ methods by 11.3 points, within a 4-10times lower training budget than the leading QAT approach. EdgeRazor delivers higher compression ratios at all bit width; the 1.58-bit Qwen3-0.6B reduces storage from 1.41 GB to 0.28 GB while accelerating decoding by 15.1times relative to the 16-bit baseline.

We introduce Delta-Aware Quantization (DAQ), a data-free post-training quantization framework that preserves the knowledge acquired during post-training. Standard quantization objectives minimize reconstruction error but are agnostic to the base model, allowing quantization noise to disproportionately corrupt the small-magnitude parameter deltas (ΔW) that encode post-training behavior -- an effect we analyze through the lens of quantization as implicit regularization. DAQ replaces reconstruction-based objectives with two delta-aware metrics -- Sign Preservation Rate and Cosine Similarity -- that directly optimize for directional fidelity of ΔW, requiring only the base and post-trained weight matrices. In a pilot FP8 study, DAQ recovers style-specific capabilities lost under standard quantization while maintaining general performance.

Vision-Language Models (VLMs) have enabled a variety of real-world applications. The large parameter size of VLMs brings large memory and computation overhead which poses significant challenges for deployment. Post-Training Quantization (PTQ) is an effective technique to reduce the memory and computation overhead. Existing PTQ methods mainly focus on large language models (LLMs), without considering the differences across other modalities. In this paper, we discover that there is a significant difference in sensitivity between language and vision tokens in large VLMs. Therefore, treating tokens from different modalities equally, as in existing PTQ methods, may over-emphasize the insensitive modalities, leading to significant accuracy loss. To deal with the above issue, we propose a simple yet effective method, Modality-Balanced Quantization (MBQ), for large VLMs. Specifically, MBQ incorporates the different sensitivities across modalities during the calibration process to minimize the reconstruction loss for better quantization parameters. Extensive experiments show that MBQ can significantly improve task accuracy by up to 4.4% and 11.6% under W3 and W4A8 quantization for 7B to 70B VLMs, compared to SOTA baselines. Additionally, we implement a W3 GPU kernel that fuses the dequantization and GEMV operators, achieving a 1.4x speedup on LLaVA-onevision-7B on the RTX 4090. The code is available at https://github.com/thu-nics/MBQ.

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point quantization and thus cannot well fit the LLM losses in this scenario. In contrast, while floating-point quantization training is more commonly implemented in production, the research on it has been relatively superficial. In this paper, we thoroughly explore the effects of floating-point quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in floating-point quantization training performance of LLM models. While presenting an accurate floating-point quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal floating-point quantization precision is directly proportional to the computational power, but within a wide computational power range, we estimate that the best cost-performance precision lies between 4-8 bits.

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.

Quantization addresses the high resource demand for large language models (LLMs) by alleviating memory pressure and bandwidth congestion and providing significantly scaled compute power with a tolerable impact on accuracy. Four-bit floating point (FP4), the lowest-precision format that preserves essential numerical properties such as exponent and sign, has begun to be adopted in cutting-edge architectures, including Blackwell and AMD CDNA, to support LLM quantization and reduce deployment costs. Although aggressive quantization can yield efficiency gains, the quantization sensitivity of within-transformer layers and whether these sensitivities generalize across existing FP4 formats and model scales remain underexplored. To elucidate quantization sensitivity, this study conducts a systematic analysis of two FP4 formats, MXFP4 and NVFP4, across three Qwen2.5 model scales (0.5B, 7B, and 14B), using controlled component-wise and block-wise isolation methodologies. We observe that MLP up- and down-projection layers consistently dominate in terms of sensitivity, while gate and attention projections are moderately and substantially less sensitive to FP4 quantization, respectively. We further find that sensitivity does not universally localize to the final blocks, but early blocks can be highly sensitive, particularly under MXFP4. Our results provide a diagnostic characterization of the inference behavior of FP4 across components, depths, and FP4 formats.

Quantization emerges as one of the most promising approaches for deploying advanced deep models on resource-constrained hardware. Mixed-precision quantization leverages multiple bit-width architectures to unleash the accuracy and efficiency potential of quantized models. However, existing mixed-precision quantization suffers exhaustive search space that causes immense computational overhead. The quantization process thus relies on separate high-performance devices rather than locally, which also leads to a significant gap between the considered hardware metrics and the real deployment.In this paper, we propose an On-chip Hardware-aware Quantization (OHQ) framework that performs hardware-aware mixed-precision quantization without accessing online devices. First, we construct the On-chip Quantization Awareness (OQA) pipeline, enabling perceive the actual efficiency metrics of the quantization operator on the hardware.Second, we propose Mask-guided Quantization Estimation (MQE) technique to efficiently estimate the accuracy metrics of operators under the constraints of on-chip-level computing power.By synthesizing network and hardware insights through linear programming, we obtain optimized bit-width configurations. Notably, the quantization process occurs on-chip entirely without any additional computing devices and data access. We demonstrate accelerated inference after quantization for various architectures and compression ratios, achieving 70% and 73% accuracy for ResNet-18 and MobileNetV3, respectively. OHQ improves latency by 15~30% compared to INT8 on deployment.

Post-training quantization (PTQ) enables efficient deployment of large language models by mapping pretrained weights to low-bit formats without retraining, typically using a small calibration set to minimize a layer-wise calibration objective. However, this sequential procedure induces a mismatch: errors from earlier quantized layers alter the inputs received by later layers, causing the activations to deviate from those of the full-precision model. Recent approaches introduce mismatch-aware calibration objectives to compensate for this effect, but leave open how much of the observed mismatch should shift each layer's calibration target. Fully applying this correction can overfit limited calibration data, while scaling the mismatch correction with a fixed coefficient ignores varying reliability of mismatch estimates across layers. To address these limitations, we propose CoreQ, a learning-free PTQ framework that applies a closed-form coefficient for mismatch correction derived from a geometric decomposition of the mismatch. The resulting coefficient adapts the correction across layers, reduces overfitting to finite calibration data, and requires no hyperparameter tuning. Given the corrected target, CoreQ minimizes the induced triangular least-squares objective with an efficient greedy successive-rounding solver and a bounded beam-search extension, K-CoreQ, that trades modest additional compute for improved performance. Across multiple LLM families, scales, bit-widths, and quantization settings, CoreQ improves perplexity and downstream accuracy over strong PTQ baselines.

We introduce a data-free quantization method for deep neural networks that does not require fine-tuning or hyperparameter selection. It achieves near-original model performance on common computer vision architectures and tasks. 8-bit fixed-point quantization is essential for efficient inference on modern deep learning hardware. However, quantizing models to run in 8-bit is a non-trivial task, frequently leading to either significant performance reduction or engineering time spent on training a network to be amenable to quantization. Our approach relies on equalizing the weight ranges in the network by making use of a scale-equivariance property of activation functions. In addition the method corrects biases in the error that are introduced during quantization. This improves quantization accuracy performance, and can be applied to many common computer vision architectures with a straight forward API call. For common architectures, such as the MobileNet family, we achieve state-of-the-art quantized model performance. We further show that the method also extends to other computer vision architectures and tasks such as semantic segmentation and object detection.

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing weights in lower bit-width formats. However, standard uniform quantization often leads to notable performance degradation, particularly in low-bit scenarios. In this work, we introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook, defined by a learnable generation matrix. To address the non-differentiability of the quantization process, we adopt Babai rounding to approximate nearest-lattice-point search during training, which enables stable optimization of the generation matrices. Once trained, decoding reduces to a simple matrix-vector multiplication, yielding an efficient and practical quantization pipeline. Experiments on multiple benchmarks show that our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines, highlighting its effectiveness in deploying large models under stringent resource constraints. Our source code is available on GitHub repository: https://github.com/xzhang9308/GLVQ.

Quantization scale and bit-width are the most important parameters when considering how to quantize a neural network. Prior work focuses on optimizing quantization scales in a global manner through gradient methods (gradient descent \& Hessian analysis). Yet, when applying perturbations to quantization scales, we observe a very jagged, highly non-smooth test loss landscape. In fact, small perturbations in quantization scale can greatly affect accuracy, yielding a 0.5-0.8% accuracy boost in 4-bit quantized vision transformers (ViTs). In this regime, gradient methods break down, since they cannot reliably reach local minima. In our work, dubbed Evol-Q, we use evolutionary search to effectively traverse the non-smooth landscape. Additionally, we propose using an infoNCE loss, which not only helps combat overfitting on the small calibration dataset (1,000 images) but also makes traversing such a highly non-smooth surface easier. Evol-Q improves the top-1 accuracy of a fully quantized ViT-Base by 10.30%, 0.78%, and 0.15% for 3-bit, 4-bit, and 8-bit weight quantization levels. Extensive experiments on a variety of CNN and ViT architectures further demonstrate its robustness in extreme quantization scenarios. Our code is available at https://github.com/enyac-group/evol-q

Quantization has been widely used to compress and accelerate inference of large language models (LLMs). Existing methods focus on exploring the per-token dynamic calibration to ensure both inference acceleration and model accuracy under 4-bit quantization. However, in autoregressive generation inference of long sequences, the overhead of repeated dynamic quantization and dequantization steps becomes considerably expensive. In this work, we propose MergeQuant, an accurate and efficient per-channel static quantization framework. MergeQuant integrates the per-channel quantization steps with the corresponding scalings and linear mappings through a Quantization Step Migration (QSM) method, thereby eliminating the quantization overheads before and after matrix multiplication. Furthermore, in view of the significant differences between the different channel ranges, we propose dimensional reconstruction and adaptive clipping to address the non-uniformity of quantization scale factors and redistribute the channel variations to the subsequent modules to balance the parameter distribution under QSM. Within the static quantization setting of W4A4, MergeQuant reduces the accuracy gap on zero-shot tasks compared to FP16 baseline to 1.3 points on Llama-2-70B model. On Llama-2-7B model, MergeQuant achieves up to 1.77x speedup in decoding, and up to 2.06x speedup in end-to-end compared to FP16 baseline.

The increasing computational demands of foundation models have spurred research into low-precision training, with 4-bit floating-point (FP4) formats emerging as a frontier for maximizing hardware throughput. While numerous techniques have been proposed to stabilize FP4 training, they often present isolated solutions with varying, and not always clear, computational overheads. This paper aims to provide a unified view of the design space of FP4 training. We introduce a comprehensive, quantisation gradient-based framework for microscaling quantization that allows for a theoretical analysis of the computational costs associated with different stabilization methods on both the forward and backward passes. Using a simulator built on this framework, we conduct an extensive empirical study across a wide range of machine learning tasks, including regression, image classification, diffusion models, and language models. By systematically evaluating thousands of combinations of techniques, such as novel gradient approximations, rounding strategies, and scaling methods, we identify which configurations offer the most favourable performance-to-overhead trade-off. We find that the techniques enabling the best trade-off involve carefully combining Hadamard transformations, tensor scaling and stochastic rounding. We further find that using UE5M3 as a scaling factor potentially offers a good compromise between range and precision with manageable computational overhead.

Quantization has become one of the most effective methodologies to compress LLMs into smaller size. However, the existing quantization solutions still show limitations of either non-negligible accuracy drop or system inefficiency. In this paper, we make a comprehensive analysis of the general quantization principles on their effect to the triangle of accuracy, memory consumption and system efficiency. We propose MixLLM that explores the new optimization space of mixed-precision quantization between output features based on the insight that different output features matter differently in the model. MixLLM identifies the output features with high salience in the global view rather than within each single layer, effectively assigning the larger bit-width to output features that need it most to achieve good accuracy with low memory consumption. We present the sweet spot of quantization configuration of algorithm-system co-design that leads to high accuracy and system efficiency. To address the system challenge, we design the two-step dequantization to make use of the int8 Tensor Core easily and fast data type conversion to reduce dequantization overhead significantly, and present the software pipeline to overlap the memory access, dequantization and the MatMul to the best. Extensive experiments show that with only 10% more bits, the PPL increasement can be reduced from about 0.5 in SOTA to within 0.2 for Llama 3.1 70B, while on average MMLU-Pro improves by 0.93 over the SOTA of three popular models. In addition to its superior accuracy, MixLLM also achieves state-of-the-art system efficiency.

Deep neural network (DNN) deployment has been confined to larger hardware devices due to their expensive computational requirements. This challenge has recently reached another scale with the emergence of large language models (LLMs). In order to reduce both their memory footprint and latency, a promising technique is quantization. It consists in converting floating point representations to low bit-width fixed point representations, usually by assuming a uniform mapping onto a regular grid. This process, referred to in the literature as uniform quantization, may however be ill-suited as most DNN weights and activations follow a bell-shaped distribution. This is even worse on LLMs whose weight distributions are known to exhibit large, high impact, outlier values. In this work, we propose an improvement over the most commonly adopted way to tackle this limitation in deep learning models quantization, namely, non-uniform quantization. NUPES leverages automorphisms to preserve the scalar multiplications. Such transformations are derived from power functions. However, the optimization of the exponent parameter and weight values remains a challenging and novel problem which could not be solved with previous post training optimization techniques which only learn to round up or down weight values in order to preserve the predictive function. We circumvent this limitation with a new paradigm: learning new quantized weights over the entire quantized space. Similarly, we enable the optimization of the power exponent, i.e. the optimization of the quantization operator itself during training by alleviating all the numerical instabilities. The resulting predictive function is compatible with integer-only low-bit inference. We show the ability of the method to achieve state-of-the-art compression rates in both, data-free and data-driven configurations.

Quantizing model weights is critical for reducing the communication and inference costs of large models. However, quantizing models -- especially to low precisions like int4 or int2 -- requires a trade-off in model quality; int2, in particular, is known to severely degrade model quality. Consequently, practitioners are often forced to maintain multiple models with different quantization levels or serve a single model that best satisfies the quality-latency trade-off. On the other hand, integer data types, such as int8, inherently possess a nested (Matryoshka) structure where smaller bit-width integers, like int4 or int2, are nested within the most significant bits. This paper proposes Matryoshka Quantization (MatQuant), a novel multi-scale quantization technique that addresses the challenge of needing multiple quantized models. It allows training and maintaining just one model, which can then be served at different precision levels. Furthermore, due to the co-training and co-distillation regularization provided by MatQuant, the int2 precision models extracted by MatQuant can be up to 10% more accurate than standard int2 quantization (using techniques like QAT or OmniQuant). This represents significant progress in model quantization, demonstrated by the fact that, with the same recipe, an int2 FFN-quantized Gemma-2 9B model is more accurate than an int8 FFN-quantized Gemma-2 2B model.

With unprecedented rapid development, deep neural networks (DNNs) have deeply influenced almost all fields. However, their heavy computation costs and model sizes are usually unacceptable in real-world deployment. Model quantization, an effective weight-lighting technique, has become an indispensable procedure in the whole deployment pipeline. The essence of quantization acceleration is the conversion from continuous floating-point numbers to discrete integer ones, which significantly speeds up the memory I/O and calculation, i.e., addition and multiplication. However, performance degradation also comes with the conversion because of the loss of precision. Therefore, it has become increasingly popular and critical to investigate how to perform the conversion and how to compensate for the information loss. This article surveys the recent five-year progress towards low-bit quantization on DNNs. We discuss and compare the state-of-the-art quantization methods and classify them into 8 main categories and 24 sub-categories according to their core techniques. Furthermore, we shed light on the potential research opportunities in the field of model quantization. A curated list of model quantization is provided at https://github.com/Kai-Liu001/Awesome-Model-Quantization.

We study weight-only post-training quantization (PTQ), which quantizes the weights of a large language model (LLM) without retraining, using little or no calibration data. Weight-only PTQ is crucial for reducing the memory footprint and latency of LLM inference, especially in memory-bound, small-batch inference scenarios, such as personalized inference on edge devices. Despite its importance, irregular weight distributions with heavy-tailed outliers in LLMs complicate quantization, recently motivating rotation-based methods that transform weights into near-Gaussian distributions, which are more regular with fewer outliers, thereby reducing quantization error. In this work, we first derive the information-theoretically optimal bit allocation for Gaussianized weights under given bit budgets, revealing that fine-grained fractional-bit quantizers approaching the Gaussian distortion-rate bound are essential to achieve near-optimal quantization performance. To bridge this theoretical insight and practical implementation, we introduce Q-Palette, a versatile collection of fractional-bit quantizers that range from trellis-coded quantizers offering near-optimal distortion to simpler vector and scalar quantizers optimized for faster inference, all efficiently implemented with optimized CUDA kernels across various bitwidths. Furthermore, leveraging Q-Palette as a foundational component, we propose a novel mixed-scheme quantization framework, jointly optimizing quantizer choices and layer fusion decisions given resource constraints. The code is available at https://github.com/snu-mllab/Q-Palette.

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.

Conventional model compression techniques for LLMs address high memory consumption and slow inference challenges but typically require computationally expensive retraining to preserve accuracy. In contrast, one-shot compression methods eliminate retraining cost, but struggle to achieve accuracy comparable to dense models. This paper presents SLIM, a new one-shot compression framework that holistically integrates hardware-friendly quantization, sparsity, and low-rank approximation into a unified process. First, we formulate the quantization process using a probabilistic approach (SLIM-Quant) that enables us to apply uniform quantization. Then, we use an existing one-shot pruning method to apply semi-structured sparsity on top of the quantized weights. Finally, to compensate for the introduced aggregated quantization and sparsity error, we use a novel saliency function with unique invertible and additive features that enables us to mathematically compute the value of low-rank adapters. SLIM improves model accuracy by up to 5.66% (LLaMA-2-7B) for 2:4 sparsity with 4-bit weight quantization, outperforming prior methods. Models compressed with SLIM achieve up to 4.3x and 3.8x on Nvidia RTX3060 and A100 GPUs, respectively. Additionally, they achieve up to 0.23x end-to-end memory reduction in comparison to their dense counterparts. We also propose an optional PEFT recipe that further improves accuracy by up to 1.66% (LLaMA-2-13B) compared to SLIM without fine-tuning.

Learning-based 3D reconstruction models, represented by Visual Geometry Grounded Transformers (VGGTs), have made remarkable progress with the use of large-scale transformers. Their prohibitive computational and memory costs severely hinder real-world deployment. Post-Training Quantization (PTQ) has become a common practice for compressing and accelerating models. However, we empirically observe that PTQ faces unique obstacles when compressing billion-scale VGGTs: the data-independent special tokens induce heavy-tailed activation distributions, while the multi-view nature of 3D data makes calibration sample selection highly unstable. This paper proposes the first Quantization framework for VGGTs, namely QuantVGGT. This mainly relies on two technical contributions: First, we introduce Dual-Smoothed Fine-Grained Quantization, which integrates pre-global Hadamard rotation and post-local channel smoothing to mitigate heavy-tailed distributions and inter-channel variance robustly. Second, we design Noise-Filtered Diverse Sampling, which filters outliers via deep-layer statistics and constructs frame-aware diverse calibration clusters to ensure stable quantization ranges. Comprehensive experiments demonstrate that QuantVGGT achieves the state-of-the-art results across different benchmarks and bit-width, surpassing the previous state-of-the-art generic quantization method with a great margin. We highlight that our 4-bit QuantVGGT can deliver a 3.7times memory reduction and 2.5times acceleration in real-hardware inference, while maintaining reconstruction accuracy above 98\% of its full-precision counterpart. This demonstrates the vast advantages and practicality of QuantVGGT in resource-constrained scenarios. Our code is released in https://github.com/wlfeng0509/QuantVGGT.

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.

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training quantization for high-performance inference. Recent works propose low-bitwidth (e.g., 8-bit or 4-bit) quantization for diffusion models, however 4-bit integer quantization typically results in low-quality images. We observe that on several widely used hardware platforms, there is little or no difference in compute capability between floating-point and integer arithmetic operations of the same bitwidth (e.g., 8-bit or 4-bit). Therefore, we propose an effective floating-point quantization method for diffusion models that provides better image quality compared to integer quantization methods. We employ a floating-point quantization method that was effective for other processing tasks, specifically computer vision and natural language tasks, and tailor it for diffusion models by integrating weight rounding learning during the mapping of the full-precision values to the quantized values in the quantization process. We comprehensively study integer and floating-point quantization methods in state-of-the-art diffusion models. Our floating-point quantization method not only generates higher-quality images than that of integer quantization methods, but also shows no noticeable degradation compared to full-precision models (32-bit floating-point), when both weights and activations are quantized to 8-bit floating-point values, while has minimal degradation with 4-bit weights and 8-bit activations.

Quantization-aware training (QAT) is essential for deploying large models under strict memory and latency constraints, yet achieving stable and robust optimization at ultra-low bitwidths remains challenging. Common approaches based on the straight-through estimator (STE) or soft quantizers often suffer from gradient mismatch, instability, or high computational overhead. As such, we propose StableQAT, a unified and efficient QAT framework that stabilizes training in ultra low-bit settings via a novel, lightweight, and theoretically grounded surrogate for backpropagation derived from a discrete Fourier analysis of the rounding operator. StableQAT strictly generalizes STE as the latter arises as a special case of our more expressive surrogate family, yielding smooth, bounded, and inexpensive gradients that improve QAT training performance and stability across various hyperparameter choices. In experiments, StableQAT exhibits stable and efficient QAT at 2-4 bit regimes, demonstrating improved training stability, robustness, and superior performance with negligible training overhead against standard QAT techniques. Our code is available at https://github.com/microsoft/StableQAT.

Model quantization is widely applied for compressing and accelerating deep neural networks (DNNs). However, conventional Quantization-Aware Training (QAT) focuses on training DNNs with uniform bit-width. The bit-width settings vary across different hardware and transmission demands, which induces considerable training and storage costs. Hence, the scheme of one-shot joint training multiple precisions is proposed to address this issue. Previous works either store a larger FP32 model to switch between different precision models for higher accuracy or store a smaller INT8 model but compromise accuracy due to using shared quantization parameters. In this paper, we introduce the Double Rounding quantization method, which fully utilizes the quantized representation range to accomplish nearly lossless bit-switching while reducing storage by using the highest integer precision instead of full precision. Furthermore, we observe a competitive interference among different precisions during one-shot joint training, primarily due to inconsistent gradients of quantization scales during backward propagation. To tackle this problem, we propose an Adaptive Learning Rate Scaling (ALRS) technique that dynamically adapts learning rates for various precisions to optimize the training process. Additionally, we extend our Double Rounding to one-shot mixed precision training and develop a Hessian-Aware Stochastic Bit-switching (HASB) strategy. Experimental results on the ImageNet-1K classification demonstrate that our methods have enough advantages to state-of-the-art one-shot joint QAT in both multi-precision and mixed-precision. We also validate the feasibility of our method on detection and segmentation tasks, as well as on LLMs task. Our codes are available at https://github.com/haiduo/Double-Rounding.

Quantizing neural networks is one of the most effective methods for achieving efficient inference on mobile and embedded devices. In particular, mixed precision quantized (MPQ) networks, whose layers can be quantized to different bitwidths, achieve better task performance for the same resource constraint compared to networks with homogeneous bitwidths. However, finding the optimal bitwidth allocation is a challenging problem as the search space grows exponentially with the number of layers in the network. In this paper, we propose QBitOpt, a novel algorithm for updating bitwidths during quantization-aware training (QAT). We formulate the bitwidth allocation problem as a constraint optimization problem. By combining fast-to-compute sensitivities with efficient solvers during QAT, QBitOpt can produce mixed-precision networks with high task performance guaranteed to satisfy strict resource constraints. This contrasts with existing mixed-precision methods that learn bitwidths using gradients and cannot provide such guarantees. We evaluate QBitOpt on ImageNet and confirm that we outperform existing fixed and mixed-precision methods under average bitwidth constraints commonly found in the literature.

Quantization-aware training (QAT) is a leading technique for improving the accuracy of quantized neural networks. Previous work has shown that decomposing training into a full-precision (FP) phase followed by a QAT phase yields superior accuracy compared to QAT alone. However, the optimal allocation of compute between the FP and QAT phases remains unclear. We conduct extensive experiments with various compute budgets, QAT bit widths, and model sizes from 86.0M to 2.2B to investigate how different QAT durations impact final performance. We demonstrate that, contrary to previous findings, the loss-optimal ratio of QAT to FP training increases with the total amount of compute. Moreover, the optimal fraction can be accurately predicted for a wide range of model sizes and quantization widths using the tokens-per-parameter-byte statistic. From experimental data, we derive a loss scaling law that predicts both optimal QAT ratios and final model performance across different QAT/FP compute allocation strategies and QAT bit widths. We use the scaling law to make further predictions, which we verify experimentally, including which QAT bit width is optimal under a given memory constraint and how QAT accuracy with different bit widths compares to full-precision model accuracy. Additionally, we propose a novel cooldown and QAT fusion approach that performs learning rate decay jointly with quantization-aware training, eliminating redundant full-precision model updates and achieving significant compute savings. These findings provide practical insights into efficient QAT planning and enable the training of higher-quality quantized models with the same compute budget.

The emergence of fine-grained numerical formats like NVFP4 presents new opportunities for efficient Large Language Model (LLM) inference. However, it is difficult to adapt existing Post-Training Quantization (PTQ) strategies to these formats: rotation-based methods compromise fine-grained block isolation; smoothing techniques struggle with significant 4-bit quantization errors; and mixed-precision approaches often conflict with hardware constraints on unified-precision computation. To address these challenges, we propose ARCQuant, a framework that boosts NVFP4 performance via Augmented Residual Channels. Distinct from methods that compromise block isolation or hardware uniformity, ARCQuant maintains a strictly unified NVFP4 format by augmenting the activation matrix with quantized residual channels. This design integrates the error compensation process directly into the matrix reduction dimension, enabling the use of standard, highly optimized GEMM kernels with minimal overhead. Theoretical analysis confirms that the worst-case error bound of our dual-stage NVFP4 quantization is comparable to that of standard 8-bit formats such as MXFP8. Extensive experiments on LLaMA and Qwen models demonstrate that ARCQuant achieves state-of-the-art accuracy, comparable to full-precision baselines in perplexity and downstream tasks. Furthermore, deployment on RTX 5090 and RTX PRO 6000 GPUs confirms practical benefits, achieving up to 3x speedup over FP16. Our code is available at https://github.com/actypedef/ARCQuant .

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based and struggle with bit widths below 8 bits. Compared to integer quantization, floating-point (FP) quantization is more flexible and can better handle long-tail or bell-shaped distributions, and it has emerged as a default choice in many hardware platforms. One characteristic of FP quantization is that its performance largely depends on the choice of exponent bits and clipping range. In this regard, we construct a strong FP-PTQ baseline by searching for the optimal quantization parameters. Furthermore, we observe a high inter-channel variance and low intra-channel variance pattern in activation distributions, which adds activation quantization difficulty. We recognize this pattern to be consistent across a spectrum of transformer models designed for diverse tasks, such as LLMs, BERT, and Vision Transformer models. To tackle this, we propose per-channel activation quantization and show that these additional scaling factors can be reparameterized as exponential biases of weights, incurring a negligible cost. Our method, for the first time, can quantize both weights and activations in the LLaMA-13B to only 4-bit and achieves an average score of 63.1 on the common sense zero-shot reasoning tasks, which is only 5.8 lower than the full-precision model, significantly outperforming the previous state-of-the-art by 12.7 points. Code is available at: https://github.com/nbasyl/LLM-FP4.

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}.

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.

Matryoshka Quantization (MatQuant) is a recent quantization approach showing that a single integer-quantized model can be served across multiple precisions, by slicing the most significant bits (MSB) at inference time. This enables a single checkpoint to cover a wide range of memory and latency budgets, but renders quantization much more challenging. In particular, the initial MatQuant relies on expensive quantization-aware training (QAT) variants, rather than fast one-shot post training quantization (PTQ), and lacks open-source and kernel support. We address all of these limitations by introducing Post-Training Matryoshka Quantization (MatGPTQ), a new PTQ pipeline that produces a single parent model jointly optimized for multiple target precisions in one-shot, based on a small calibration set. MatGPTQ casts Matryoshka quantization as a multi-precision objective with bit-slicing and cross-bit error compensation, resulting in an algorithm that produces a multi-bit-width, "sliceable" model in a single pass. We also incorporate a new budget-aware search for heterogeneous per-layer bit-witdhs and provide efficient kernels that implement slicing and mixed-precision execution. Across standard LLMs and benchmarks, MatGPTQ preserves high-bit accuracy while substantially improving performance at low-bit-witdh settings. Overall, we establish a new state of the art for Matryoshka-style post-training quantization and make single-checkpoint, multi-precision deployment open and practical. Code is available at https://github.com/IST-DASLab/MatGPTQ.

Quantization is a practical technique for making large language models easier to deploy by reducing the precision used to store and operate on model weights. This can lower memory use and improve runtime feasibility on constrained hardware, which is especially relevant for users running models locally. Quantization in llama.cpp enables large language models to run on commodity hardware, but available formats are often evaluated inconsistently, making it hard to choose among schemes. We present a unified empirical study of the llama.cpp quantization on a single modern model, Llama-3.1-8B-Instruct (FP16, GGUF), covering 3-8 bit K-quant and legacy formats. We evaluate downstream task performance across standard reasoning, knowledge, instruction-following, and truthfulness benchmarks, and also measure perplexity and CPU throughput (prefill/decoding) alongside model size, compression, and quantization time. Ultimately, this work is a practical guide for choosing a llama.cpp quantization scheme, helping readers make informed, context-aware decisions for their intended use and resource budget.

Quantization methods reduce the number of bits required to represent each parameter in a model, trading accuracy for smaller memory footprints and inference latencies. However, the final model size depends on both the number of parameters of the original model and the rate of compression. For example, a 30B 8-bit model and a 60B 4-bit model have the same number of bits but may have very different zero-shot accuracies. In this work, we study this trade-off by developing inference scaling laws of zero-shot performance in Large Language Models (LLMs) to determine the bit-precision and model size that maximizes zero-shot performance. We run more than 35,000 experiments with 16-bit inputs and k-bit parameters to examine which zero-shot quantization methods improve scaling for 3 to 8-bit precision at scales of 19M to 176B parameters across the LLM families BLOOM, OPT, NeoX/Pythia, and GPT-2. We find that it is challenging to improve the bit-level scaling trade-off, with the only improvements being the use of a small block size -- splitting the parameters into small independently quantized blocks -- and the quantization data type being used (e.g., Int vs Float). Overall, our findings show that {4-bit} precision is almost universally optimal for total model bits and zero-shot accuracy.

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.

Serving LLMs requires substantial memory due to the storage requirements of Key-Value (KV) embeddings in the KV cache, which grows with sequence length. An effective approach to compress KV cache is quantization. However, traditional quantization methods face significant memory overhead due to the need to store quantization constants (at least a zero point and a scale) in full precision per data block. Depending on the block size, this overhead can add 1 or 2 bits per quantized number. We introduce QJL, a new quantization approach that consists of a Johnson-Lindenstrauss (JL) transform followed by sign-bit quantization. In contrast to existing methods, QJL eliminates memory overheads by removing the need for storing quantization constants. We propose an asymmetric estimator for the inner product of two vectors and demonstrate that applying QJL to one vector and a standard JL transform without quantization to the other provides an unbiased estimator with minimal distortion. We have developed an efficient implementation of the QJL sketch and its corresponding inner product estimator, incorporating a lightweight CUDA kernel for optimized computation. When applied across various LLMs and NLP tasks to quantize the KV cache to only 3 bits, QJL demonstrates a more than fivefold reduction in KV cache memory usage without compromising accuracy, all while achieving faster runtime. Codes are available at https://github.com/amirzandieh/QJL.

Quantization is a proven effective method for compressing large language models. Although popular techniques like W8A8 and W4A16 effectively maintain model performance, they often fail to concurrently speed up the prefill and decoding stages of inference. W4A8 is a promising strategy to accelerate both of them while usually leads to a significant performance degradation. To address these issues, we present QQQ, a Quality Quattuor-bit Quantization method with 4-bit weights and 8-bit activations. QQQ employs adaptive smoothing and Hessian-based compensation, significantly enhancing the performance of quantized models without extensive training. Furthermore, we meticulously engineer W4A8 GEMM kernels to increase inference speed. Our specialized per-channel W4A8 GEMM and per-group W4A8 GEMM achieve impressive speed increases of 3.67times and 3.29 times over FP16 GEMM. Our extensive experiments show that QQQ achieves performance on par with existing state-of-the-art LLM quantization methods while significantly accelerating inference, achieving speed boosts up to 2.24 times, 2.10times, and 1.25times compared to FP16, W8A8, and W4A16, respectively.

We compress KV cache entries by quantizing angles in the Fast Walsh-Hadamard domain, where a random diagonal rotation makes consecutive element pairs approximately uniformly distributed on the unit circle. We extend this angular quantizer with per-layer early-boost, which independently configures K and V codebook sizes at each layer, allocating higher precision to a model-specific subset of critical layers. Across seven models (1B to 7B parameters), per-layer early-boost achieves lossless compression on four models and near-lossless quality on six of seven, at 3.28 to 3.67 angle bits per element. Asymmetric norm quantization (8-bit for keys, 4-bit log-space for values) yields 6.56 total bits per element on Mistral-7B with perplexity degradation of +0.0014 and no calibration data. A layer-group sensitivity analysis reveals model-specific bottleneck patterns, including K-dominated versus V-dominated layers and negative-transfer layers where increased precision degrades quality.

Prevailing quantization techniques in Learned Image Compression (LIC) typically employ a static, uniform bit-width across all layers, failing to adapt to the highly diverse data distributions and sensitivity characteristics inherent in LIC models. This leads to a suboptimal trade-off between performance and efficiency. In this paper, we introduce DynaQuant, a novel framework for dynamic mixed-precision quantization that operates on two complementary levels. First, we propose content-aware quantization, where learnable scaling and offset parameters dynamically adapt to the statistical variations of latent features. This fine-grained adaptation is trained end-to-end using a novel Distance-aware Gradient Modulator (DGM), which provides a more informative learning signal than the standard Straight-Through Estimator. Second, we introduce a data-driven, dynamic bit-width selector that learns to assign an optimal bit precision to each layer, dynamically reconfiguring the network's precision profile based on the input data. Our fully dynamic approach offers substantial flexibility in balancing rate-distortion (R-D) performance and computational cost. Experiments demonstrate that DynaQuant achieves rd performance comparable to full-precision models while significantly reducing computational and storage requirements, thereby enabling the practical deployment of advanced LIC on diverse hardware platforms.

Product quantization (PQ) is a widely used technique for ad-hoc retrieval. Recent studies propose supervised PQ, where the embedding and quantization models can be jointly trained with supervised learning. However, there is a lack of appropriate formulation of the joint training objective; thus, the improvements over previous non-supervised baselines are limited in reality. In this work, we propose the Matching-oriented Product Quantization (MoPQ), where a novel objective Multinoulli Contrastive Loss (MCL) is formulated. With the minimization of MCL, we are able to maximize the matching probability of query and ground-truth key, which contributes to the optimal retrieval accuracy. Given that the exact computation of MCL is intractable due to the demand of vast contrastive samples, we further propose the Differentiable Cross-device Sampling (DCS), which significantly augments the contrastive samples for precise approximation of MCL. We conduct extensive experimental studies on four real-world datasets, whose results verify the effectiveness of MoPQ. The code is available at https://github.com/microsoft/MoPQ.

Large language models (LLMs) achieve impressive performance across domains but face significant challenges when deployed on consumer-grade GPUs or personal devices such as laptops, due to high memory consumption and inference costs. Post-training quantization (PTQ) of LLMs offers a promising solution that reduces their memory footprint and decoding latency. In practice, PTQ with uniform quantization representation is favored for its efficiency and ease of deployment since uniform quantization is widely supported by mainstream hardware and software libraries. Recent studies on geq 2-bit uniform quantization have led to noticeable improvements in post-quantization model performance; however, they primarily focus on quantization methodologies, while the initialization of quantization parameters is underexplored and still relies on the suboptimal Min-Max strategies. In this work, we propose NeUQI, a method devoted to efficiently determining near-optimal initial parameters for uniform quantization. NeUQI is orthogonal to prior quantization methodologies and can seamlessly integrate with them. The experiments with the LLaMA and Qwen families on various tasks demonstrate that our NeUQI consistently outperforms existing methods. Furthermore, when combined with a lightweight distillation strategy, NeUQI can achieve superior performance to PV-tuning, a much more resource-intensive approach.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

Post-training quantization for reducing the storage of deep neural network models has been demonstrated to be an effective way in various tasks. However, low-bit quantization while maintaining model accuracy is a challenging problem. In this paper, we present a range estimation method to improve the quantization performance for post-training quantization. We model the range estimation into an optimization problem of minimizing quantization errors by layer-wise local minima. We prove this problem is locally convex and present an efficient search algorithm to find the optimal solution. We propose the application of the above search algorithm to the transformed weights space to do further improvement in practice. Our experiments demonstrate that our method outperforms state-of-the-art performance generally on top-1 accuracy for image classification tasks on the ResNet series models and Inception-v3 model. The experimental results show that the proposed method has almost no loss of top-1 accuracy in 8-bit and 6-bit settings for image classifications, and the accuracy of 4-bit quantization is also significantly improved. The code is available at https://github.com/codeiscommitting/REQuant.

Deep neural networks (DNNs) are ubiquitous in computer vision and natural language processing, but suffer from high inference cost. This problem can be addressed by quantization, which consists in converting floating point operations into a lower bit-width format. With the growing concerns on privacy rights, we focus our efforts on data-free methods. However, such techniques suffer from their lack of adaptability to the target devices, as a hardware typically only support specific bit widths. Thus, to adapt to a variety of devices, a quantization method shall be flexible enough to find good accuracy v.s. speed trade-offs for every bit width and target device. To achieve this, we propose REx, a quantization method that leverages residual error expansion, along with group sparsity and an ensemble approximation for better parallelization. REx is backed off by strong theoretical guarantees and achieves superior performance on every benchmarked application (from vision to NLP tasks), architecture (ConvNets, transformers) and bit-width (from int8 to ternary quantization).

Quantization is a crucial technique for deploying deep learning models on resource-constrained devices, such as embedded FPGAs. Prior efforts mostly focus on quantizing matrix multiplications, leaving other layers like BatchNorm or shortcuts in floating-point form, even though fixed-point arithmetic is more efficient on FPGAs. A common practice is to fine-tune a pre-trained model to fixed-point for FPGA deployment, but potentially degrading accuracy. This work presents QFX, a novel trainable fixed-point quantization approach that automatically learns the binary-point position during model training. Additionally, we introduce a multiplier-free quantization strategy within QFX to minimize DSP usage. QFX is implemented as a PyTorch-based library that efficiently emulates fixed-point arithmetic, supported by FPGA HLS, in a differentiable manner during backpropagation. With minimal effort, models trained with QFX can readily be deployed through HLS, producing the same numerical results as their software counterparts. Our evaluation shows that compared to post-training quantization, QFX can quantize models trained with element-wise layers quantized to fewer bits and achieve higher accuracy on both CIFAR-10 and ImageNet datasets. We further demonstrate the efficacy of multiplier-free quantization using a state-of-the-art binarized neural network accelerator designed for an embedded FPGA (AMD Xilinx Ultra96 v2). We plan to release QFX in open-source format.

Diffusion Models (DM) have democratized AI image generation through an iterative denoising process. Quantization is a major technique to alleviate the inference cost and reduce the size of DM denoiser networks. However, as denoisers evolve from variants of convolutional U-Nets toward newer Transformer architectures, it is of growing importance to understand the quantization sensitivity of different weight layers, operations and architecture types to performance. In this work, we address this challenge with Qua^2SeDiMo, a mixed-precision Post-Training Quantization framework that generates explainable insights on the cost-effectiveness of various model weight quantization methods for different denoiser operation types and block structures. We leverage these insights to make high-quality mixed-precision quantization decisions for a myriad of diffusion models ranging from foundational U-Nets to state-of-the-art Transformers. As a result, Qua^2SeDiMo can construct 3.4-bit, 3.9-bit, 3.65-bit and 3.7-bit weight quantization on PixArt-{alpha}, PixArt-{Sigma}, Hunyuan-DiT and SDXL, respectively. We further pair our weight-quantization configurations with 6-bit activation quantization and outperform existing approaches in terms of quantitative metrics and generative image quality.

The Segment Anything Model 2 (SAM2) is a powerful foundation model for promptable segmentation. However, its high computational and memory costs are a major barrier to deployment on resource-constrained devices. In this paper, we present Q-SAM2, an accurate low-bit quantization method that achieves high compression and high fidelity. To address performance degradation arising from challenging weight and activation distributions during quantization, Q-SAM2 introduces two novel contributions: Variance-Reduced Calibration (VRC), an initialization method that reduces weight statistical variance by minimizing the Frobenius norm over a small calibration batch; and Learnable Statistical Clipping (LSC), a Quantization-Aware Training (QAT) method that learns momentum-stabilized clipping factors to manage outliers in weights and activations. Comprehensive experiments demonstrate that Q-SAM2 achieves highly accurate inference with substantial efficiency gains, significantly surpassing state-of-the-art general QAT schemes, particularly in the ultra-low 2-bit regime. Specifically, Q-SAM2 achieves an accuracy gain of up to 9.7 ppt in J&F on the video segmentation benchmark and 7.3 ppt in mIoU for instance segmentation over the best competing QAT model, all while achieving an 8x reduction in model size compared to the BF16 baseline.

While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. To that end, we generalize a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism. Among other things, we propose modifications to promote sparsity of the weights, and rigorously analyze the associated error. Additionally, our error analysis expands the results of previous work on GPFQ to handle general quantization alphabets, showing that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures thereby also extending previous results. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy compared to unquantized models. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.

Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse natural language processing tasks. However, their extensive memory requirements, particularly due to KV cache growth during long-text understanding and generation, present significant challenges for deployment in resource-constrained environments. Quantization has emerged as a promising solution to reduce memory consumption while preserving historical information. We propose XQuant, a training-free and plug-and-play framework that achieves ultra-low equivalent bit-width KV cache quantization. XQuant introduces two key innovations: a computationally negligible data-free calibration method and cross-layer KV cache compression, enabling quantization to sub-1.4 bits. Extensive experiments on TruthfulQA and LongBench demonstrate that XQuant outperforms state-of-the-art methods (e.g., KIVI-2bit and AsymKV-1.5bit) by achieving lower bit-width while maintaining superior performance, establishing a better trade-off between memory efficiency and model accuracy.

Post-training quantization (PTQ) is a practical path to deploy large diffusion models, but quantization noise can accumulate over the denoising trajectory and degrade generation quality. We propose Q-Drift, a principled sampler-side correction that treats quantization error as an implicit stochastic perturbation on each denoising step and derives a marginal-distribution-preserving drift adjustment. Q-Drift estimates a timestep-wise variance statistic from calibration, in practice requiring as few as 5 paired full-precision/quantized calibration runs. The resulting sampler correction is plug-and-play with common samplers, diffusion models, and PTQ methods, while incurring negligible overhead at inference. Across six diverse text-to-image models (spanning DiT and U-Net), three samplers (Euler, flow-matching, DPM-Solver++), and two PTQ methods (SVDQuant, MixDQ), Q-Drift improves FID over the corresponding quantized baseline in most settings, with up to 4.59 FID reduction on PixArt-Sigma (SVDQuant W3A4), while preserving CLIP scores.

The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms. The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2. Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error, minimizing the Frobenius and spectral norms of the weight approximation error. Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results. However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms. In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA), and offer a closed-form solution to the problem. We show QERA benefits both existing low-precision fine-tuning and inference methods -- QERA achieves a fine-tuned accuracy gain of Δ_{acc} = 6.05% of 2-bit RoBERTa-base on GLUE compared to LoftQ; and obtains Δ_{acc} = 2.97% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and Δ_{ppl} = - 0.28 lower perplexity on WikiText2 than LQER.

NVFP4 has grown increasingly popular as a 4-bit format for quantizing large language models due to its hardware support and its ability to retain useful information with relatively few bits per parameter. However, the format is not without limitations: recent work has shown that NVFP4 suffers from its error distribution, resulting in large amounts of quantization error on near-maximal values in each group of 16 values. In this work, we leverage this insight to design new Adaptive Block-Scaled Data Types that can adapt to the distribution of their input values. For four-bit quantization, our proposed IF4 (Int/Float 4) data type selects between FP4 and INT4 representations for each group of 16 values, which are then scaled by an E4M3 scale factor as is done with NVFP4. The selected data type is denoted using the scale factor's sign bit, which is currently unused in NVFP4, and we apply the same insight to design formats for other bit-widths, including IF3 and IF6. When used to quantize language models, we find that IF4 outperforms existing 4-bit block-scaled formats, achieving lower loss during quantized training and achieving higher accuracy on many tasks in post-training quantization. We additionally design and evaluate an IF4 Multiply-Accumulate (MAC) unit to demonstrate that IF4 can be implemented efficiently in next-generation hardware accelerators. Our code is available at https://github.com/mit-han-lab/fouroversix.

The rapid scaling of language models (LMs) has resulted in unprecedented computational, memory, and energy requirements, making their training and deployment increasingly unsustainable. Quantization has emerged as an essential compression technique to reduce model size, alleviate memory bottlenecks, and accelerate inference. However, while uniform low-bit quantization (e.g., INT8, INT4) provides significant efficiency gains, it can degrade accuracy in sensitive components of transformer-based LMs. Mixed-precision quantization offers a promising alternative by selectively allocating precision across layers or within tensors to balance efficiency and accuracy. This survey provides a comprehensive overview of Mixed-Precision quantization frameworks for LMs (MXPLMs). We first review quantization fundamentals, including uniform and non-uniform quantizers, quantization granularity, and methods widely used in post-training quantization. We then categorize and compare recent MXPLM frameworks according to their bit allocation strategies and precision configurations across weights, activations, and key-value caches. A comparative analysis highlights differences in perplexity, zero-shot task performance, and deployment trade-offs. Furthermore, we contrast MXPLMs with earlier mixed-precision quantization methods for deep neural networks, identifying strategies that transfer and those that face challenges in the LM setting. Finally, we summarize open issues and future directions, including hardware-aware design, activation quantization, and scalable optimization methods for billion-parameter models. By consolidating recent advances, this work serves as a reference for understanding the current landscape and research prospects of mixed-precision quantization for large-scale language models.

When quantizing neural networks for efficient inference, low-bit integers are the go-to format for efficiency. However, low-bit floating point numbers have an extra degree of freedom, assigning some bits to work on an exponential scale instead. This paper in-depth investigates this benefit of the floating point format for neural network inference. We detail the choices that can be made for the FP8 format, including the important choice of the number of bits for the mantissa and exponent, and show analytically in which settings these choices give better performance. Then we show how these findings translate to real networks, provide an efficient implementation for FP8 simulation, and a new algorithm that enables the learning of both the scale parameters and the number of exponent bits in the FP8 format. Our chief conclusion is that when doing post-training quantization for a wide range of networks, the FP8 format is better than INT8 in terms of accuracy, and the choice of the number of exponent bits is driven by the severity of outliers in the network. We also conduct experiments with quantization-aware training where the difference in formats disappears as the network is trained to reduce the effect of outliers.

Searching for approximate nearest neighbors (ANN) in the high-dimensional Euclidean space is a pivotal problem. Recently, with the help of fast SIMD-based implementations, Product Quantization (PQ) and its variants can often efficiently and accurately estimate the distances between the vectors and have achieved great success in the in-memory ANN search. Despite their empirical success, we note that these methods do not have a theoretical error bound and are observed to fail disastrously on some real-world datasets. Motivated by this, we propose a new randomized quantization method named RaBitQ, which quantizes D-dimensional vectors into D-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations. Extensive experiments on real-world datasets confirm that (1) our method outperforms PQ and its variants in terms of accuracy-efficiency trade-off by a clear margin and (2) its empirical performance is well-aligned with our theoretical analysis.

Deep convolutional neural networks (DCNNs) have shown dominant performance in the task of super-resolution (SR). However, their heavy memory cost and computation overhead significantly restrict their practical deployments on resource-limited devices, which mainly arise from the floating-point storage and operations between weights and activations. Although previous endeavors mainly resort to fixed-point operations, quantizing both weights and activations with fixed coding lengths may cause significant performance drop, especially on low bits. Specifically, most state-of-the-art SR models without batch normalization have a large dynamic quantization range, which also serves as another cause of performance drop. To address these two issues, we propose a new quantization scheme termed PArameterized Max Scale (PAMS), which applies the trainable truncated parameter to explore the upper bound of the quantization range adaptively. Finally, a structured knowledge transfer (SKT) loss is introduced to fine-tune the quantized network. Extensive experiments demonstrate that the proposed PAMS scheme can well compress and accelerate the existing SR models such as EDSR and RDN. Notably, 8-bit PAMS-EDSR improves PSNR on Set5 benchmark from 32.095dB to 32.124dB with 2.42times compression ratio, which achieves a new state-of-the-art.

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/.

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.

We demonstrate, for the first time, fully quantized training (FQT) of large language models (LLMs) using predominantly 4-bit floating-point (FP4) precision for weights, activations, and gradients on datasets up to 200 billion tokens. We extensively investigate key design choices for FP4, including block sizes, scaling formats, and rounding methods. Our analysis shows that the NVFP4 format, where each block of 16 FP4 values (E2M1) shares a scale represented in E4M3, provides optimal results. We use stochastic rounding for backward and update passes and round-to-nearest for the forward pass to enhance stability. Additionally, we identify a theoretical and empirical threshold for effective quantized training: when the gradient norm falls below approximately 3 times the quantization noise, quantized training becomes less effective. Leveraging these insights, we successfully train a 7-billion-parameter model on 256 Intel Gaudi2 accelerators. The resulting FP4-trained model achieves downstream task performance comparable to a standard BF16 baseline, confirming that FP4 training is a practical and highly efficient approach for large-scale LLM training. A reference implementation is supplied in https://github.com/Anonymous1252022/fp4-all-the-way .

Quantization to low bitwidth is a standard approach for deploying large language models, however, a few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer. A common mitigation approach is to apply some fixed orthogonal transforms, such as Hadamard matrices, before quantization, which typically reduces the dynamic range. Yet, these transforms ignore the statistics of the data, and their optimality is currently not understood. In this work, we derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization using standard data-free quantizers for common numerical formats. Specifically, we provide derivations of the optimal adaptive (data-aware) transforms for round-to-nearest (RTN), AbsMax-scaled block quantizers for both integer and floating-point formats. The resulting construction, which we call WUSH, combines a Hadamard backbone with a data-dependent component based on second-order moments, yielding a non-orthogonal transform that is provably optimal under mild assumptions and remains structured for efficient implementation. Preliminary experimental results show that our approach consistently improves upon the Hadamard transform for common formats.

Current state-of-the-art results in computer vision depend in part on fine-tuning large pre-trained vision models. However, with the exponential growth of model sizes, the conventional full fine-tuning, which needs to store a individual network copy for each tasks, leads to increasingly huge storage and transmission overhead. Adapter-based Parameter-Efficient Tuning (PET) methods address this challenge by tuning lightweight adapters inserted into the frozen pre-trained models. In this paper, we investigate how to make adapters even more efficient, reaching a new minimum size required to store a task-specific fine-tuned network. Inspired by the observation that the parameters of adapters converge at flat local minima, we find that adapters are resistant to noise in parameter space, which means they are also resistant to low numerical precision. To train low-precision adapters, we propose a computational-efficient quantization method which minimizes the quantization error. Through extensive experiments, we find that low-precision adapters exhibit minimal performance degradation, and even 1-bit precision is sufficient for adapters. The experimental results demonstrate that 1-bit adapters outperform all other PET methods on both the VTAB-1K benchmark and few-shot FGVC tasks, while requiring the smallest storage size. Our findings show, for the first time, the significant potential of quantization techniques in PET, providing a general solution to enhance the parameter efficiency of adapter-based PET methods. Code: https://github.com/JieShibo/PETL-ViT