Daily Papers

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.

Mixed-precision post-training quantization needs a per-module sensitivity signal; for a text embedder the obvious one -- the retrieval quality a module costs when quantized -- needs relevance labels that deployments rarely have. We measure a label-free substitute: quantization-induced representation drift, obtained by quantizing one module, re-encoding the corpus, and recording how far the output embeddings moved from their full-precision positions. What is specific is the observable: the deployed output representation a dense retriever ranks with. Across five development embedders, configuration-level drift orders sampled mixed-precision plans against held-out retrieval quality at a macro Spearman of 0.911, the sensitivity transports across calibration corpora and retrieval domains in the usable regime, module drifts compose rank-consistently but not numerically, and relevance-derived sensitivity adds no consistent value. The method is one additive allocation under a hard packed-byte budget, with no labels and no search. On three embedders held untouched until method, baselines and hypotheses were frozen and sealed, the pre-registered directional hypothesis against the prior LieQ criterion holds (3/3 at the main budget, no collapse) and drift scores above a two-sided LieQ steelman in 2/3; but at the main budget drift is numerically lower than same-budget uniform precision on all three (-0.99, -0.85, -1.01 points), having reduced module and whole-model drift as designed. Output drift is thus a robust coarse sensitivity signal, not a universally optimal allocation objective: it avoids the catastrophic failures of the transferred signed-geometry adaptation and can remain usable at stressed budgets where uniform collapses, but fine-grained redistribution around a strong uniform operating point remains unresolved.

Mixed-precision post-training quantization is a network compression method that assigns bits layer by layer, under a global memory budget using a small calibration set. The main difficulties are to overcome the combinatorial nature of the allocation problem and to manage the sensitivity to small, potentially corrupted databases. Hence, an efficient allocation method should be fast to compute and preserve model quality when calibration data are corrupted. To design such a method, we derive a layerwise probabilistic analysis of the quantization error that separates propagated error from the local perturbation introduced at a given layer. We use this local term to build a separable score for a simple allocation algorithm, that requires no external solver. The probabilistic nature of our approach brings robustness to corrupted data. On denoising tasks with DRUNet, with an average budget of 4 bits per weight, our method matches or improves state-of-the-art mixed-precision baselines under clean calibration, and is more robust to corrupted calibration, with PSNR gains of up to 7.5 dB under the tested corruptions. Experiments show bit-allocation speed-ups from 28x to 2,570x over the studied baselines. For quantized diffusion models, our experiments show that a direct application of our framework also improves the state-of-the-art.

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

While vision transformers (ViTs) have shown great potential in computer vision tasks, their intense computation and memory requirements pose challenges for practical applications. Existing post-training quantization methods leverage value redistribution or specialized quantizers to address the non-normal distribution in ViTs. However, without considering the asymmetry in activations and relying on hand-crafted settings, these methods often struggle to maintain performance under low-bit quantization. To overcome these challenges, we introduce SmoothQuant with bias term (SQ-b) to alleviate the asymmetry issue and reduce the clamping loss. We also introduce optimal scaling factor ratio search (OPT-m) to determine quantization parameters by a data-dependent mechanism automatically. To further enhance the compressibility, we incorporate the above-mentioned techniques and propose a mixed-precision post-training quantization framework for vision transformers (MPTQ-ViT). We develop greedy mixed-precision quantization (Greedy MP) to allocate layer-wise bit-width considering both model performance and compressibility. Our experiments on ViT, DeiT, and Swin demonstrate significant accuracy improvements compared with SOTA on the ImageNet dataset. Specifically, our proposed methods achieve accuracy improvements ranging from 0.90% to 23.35% on 4-bit ViTs with single-precision and from 3.82% to 78.14% on 5-bit fully quantized ViTs with mixed-precision.

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

Vision-Language-Action (VLA) models exhibit remarkable action generation for embodied intelligence, but their heavy compute make deployment on edge platforms impractical. Aggressive, sub-4-bit weight quantization is the natural solution, yet existing post-training quantization (PTQ) methods suffer severe performance degradation in this regime. To address this, we introduce ActQuant, an action-guided mixed-precision PTQ framework that operates in two stages: (1) an inter-tensor bit allocator that assigns each weight matrix a single bit-width based on how much it contributes to predicting the agent's actions; (2) an intra-tensor scale optimizer tunes per-block quantization scales using action-aware curvature, so that dynamic range is concentrated on the weights most influential for control. To deliver the on-device benefits of our aggressive quantization, we further introduce OmniModel.cpp, an agentic conversion pipeline that ports architectures into a native C/C++ runtime with efficient low-bit kernels. We evaluate ActQuant both in simulation and on a real-world 6-DoF UR3 arm, with all models deployed through OmniModel.cpp. On the LIBERO benchmark, ActQuant is the only method that operates at or below 3 bits-per-weight, retaining 95.0% on OpenVLA-OFT and 94.8% on π_{0.5}. Pushed further, ActQuant reaches 2.5 bpw at 90.1% on OpenVLA-OFT, compressing the backbone from 14.3 GB to 2.7 GB (5.3times). On the physical UR3 arm, π_{0.5} quantized with ActQuant retains the baseline's success rate while reducing the memory footprint by 2.5times.

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.

Post-Training Quantization (PTQ) is pivotal for deploying large language models (LLMs) within resource-limited settings by significantly reducing resource demands. However, existing PTQ strategies underperform at low bit levels < 3 bits due to the significant difference between the quantized and original weights. To enhance the quantization performance at low bit widths, we introduce a Mixed-precision Graph Neural PTQ (MG-PTQ) approach, employing a graph neural network (GNN) module to capture dependencies among weights and adaptively assign quantization bit-widths. Through the information propagation of the GNN module, our method more effectively captures dependencies among target weights, leading to a more accurate assessment of weight importance and optimized allocation of quantization strategies. Extensive experiments on the WikiText2 and C4 datasets demonstrate that our MG-PTQ method outperforms previous state-of-the-art PTQ method GPTQ, setting new benchmarks for quantization performance under low-bit conditions.

Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33\% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3\times speedup over 16-bit baseline. Code is available at https://github.com/utkarsh-dmx/project-resq.

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 is essential for deploying large language models (LLMs) on resource constrained hardware, yet state of the art methods enforce uniform bit widths across layers, yielding suboptimal accuracy efficiency trade offs. We present RAMP (Reinforcement Adaptive Mixed Precision), an off policy Soft Actor Critic framework that learns per layer bit width assignments to minimize perplexity under a global bit budget. The policy conditions on an 11 dimensional embedding of activation statistics, weight properties, and structural descriptors, enabling zero shot transfer across model families and scales. To enable stable sub 4 bit quantization, we introduce Scale Folding, a preconditioning technique that migrates activation outliers into weights via per channel scaling and normalization layer compensation. A quality prioritized reward with asymmetric penalties and budget cliffs drives rapid convergence. On Llama 2 7B, RAMP achieves 5.54 perplexity at 3.68GB (3.65 effective bits), outperforming uniform 4 bit AWQ (5.60 at 3.90 GB) and GPTQ by 6% in size and 1% to3% in quality. Critically, a policy trained only on Llama 2 7B generalizes zero shot to Llama 2 13B and Mistral 7B, often surpassing target specific training, supporting the hypothesis that quantization sensitivity is primarily architectural. The HALO pipeline exports allocations to GGUF format for kernel free inference on CPUs, GPUs, and edge devices, retaining 99.5% of FP16 commonsense reasoning performance.

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

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.

Diffusion transformers have demonstrated remarkable capabilities in generating videos. However, their practical deployment is severely constrained by high memory usage and computational cost. Post-Training Quantization provides a practical way to reduce memory usage and boost computation speed. Existing quantization methods typically apply a static bit-width allocation, overlooking the quantization difficulty of activations across diffusion timesteps, leading to a suboptimal trade-off between efficiency and quality. In this paper, we propose a inference time NVFP4/INT8 Mixed-Precision Quantization framework. We find a strong linear correlation between a block's input-output difference and the quantization sensitivity of its internal linear layers. Based on this insight, we design a lightweight predictor that dynamically allocates NVFP4 to temporally stable layers to maximize memory compression, while selectively preserving INT8 for volatile layers to ensure robustness. This adaptive precision strategy enables aggressive quantization without compromising generation quality. Beside this, we observe that the residual between the input and output of a Transformer block exhibits high temporal consistency across timesteps. Leveraging this temporal redundancy, we introduce Temporal Delta Cache (TDC) to skip computations for these invariant blocks, further reducing the computational cost. Extensive experiments demonstrate that our method achieves 1.92times end-to-end acceleration and 3.32times memory reduction, setting a new baseline for efficient inference in Video DiTs.

Mixture-of-Experts (MoE) is a promising way to scale up the learning capacity of large language models. It increases the number of parameters while keeping FLOPs nearly constant during inference through sparse activation. Yet, it still suffers from significant memory overheads due to the vast parameter size, necessitating model compression techniques. Post-training quantization offers a powerful approach for model compression. Existing methods adopt a fixed quantization precision for the entire MoE model. This rigid setup can lead to suboptimal performance, without considering the inherent sparse structure. For example, MoE's sparse routing mechanism leads to different activation patterns, where shared experts are accessed by all tokens while token-conditioned experts are selectively activated. This activation disparity suggests different quantization requirements, with consistently activated shared experts potentially needing higher precision to maintain model quality. In this paper, we study a fine-grained precision setup for MoE quantization. We explore MoE structure-aware quantization heuristics, ranging from coarse (e.g., MoE layers) to fine granularity (e.g., linear layers). Our investigations reveal critical principles, where different MoE structures require varying numbers of bits for effective quantization. Conclusions are supported by extensive benchmarking across two representative MoE models and six tasks including commonsense reasoning and natural language understanding. We further show that an MoE quantized in a fined-grained mixed precision achieved state-of-the-art 65.35% performance on average compared to the baseline 64.30% (i.e., GPTQ). Moreover, based on the findings, we introduce novel data-driven techniques for optimizing bit allocation in MoE quantization, including the outlier-aware linear layer scorer and MoE block importance predictor.

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

Fine-grained mixed-precision quantization promises efficient large language model inference, but local precision choices can conflict with regular GPU storage and computation units. This precision-boundary mismatch limits the translation of compression into practical acceleration. We introduce AlignQuant, a post-training quantization method that uses GPU-compatible two-dimensional weight tiles as the common unit of precision allocation, compact storage, and execution. This shared partition lets precision follow sensitivity within output channels. Joint prefill/decode calibration scores precision reductions using projection-output perturbations weighted by language-model loss gradients under quantized activations. Phase-normalized scores prioritize higher precision for tiles important to either phase under a model-wide weight-storage budget. Each tile stores one selected representation, while phase-specialized kernels reuse the packed model and expand lower-bit weights for INT8 computation with 8-bit activations. Across four LLMs spanning 3B to 14B parameters, AlignQuant achieves up to 2.50times generation speedup over BF16 while preserving model quality. Evaluations further cover three GPUs and contexts up to 64K tokens. These results show that local precision flexibility and regular GPU execution can coexist through a shared tile unit. The implementation is available at https://github.com/HanzhiZhang-Ulrica/AlignQuant.

Vision transformers (ViTs) have demonstrated remarkable performance across various visual tasks. However, ViT models suffer from substantial computational and memory requirements, making it challenging to deploy them on resource-constrained platforms. Quantization is a popular approach for reducing model size, but most studies mainly focus on equal bit-width quantization for the entire network, resulting in sub-optimal solutions. While there are few works on mixed precision quantization (MPQ) for ViTs, they typically rely on search space-based methods or employ mixed precision arbitrarily. In this paper, we introduce LRP-QViT, an explainability-based method for assigning mixed-precision bit allocations to different layers based on their importance during classification. Specifically, to measure the contribution score of each layer in predicting the target class, we employ the Layer-wise Relevance Propagation (LRP) method. LRP assigns local relevance at the output layer and propagates it through all layers, distributing the relevance until it reaches the input layers. These relevance scores serve as indicators for computing the layer contribution score. Additionally, we have introduced a clipped channel-wise quantization aimed at eliminating outliers from post-LayerNorm activations to alleviate severe inter-channel variations. To validate and assess our approach, we employ LRP-QViT across ViT, DeiT, and Swin transformer models on various datasets. Our experimental findings demonstrate that both our fixed-bit and mixed-bit post-training quantization methods surpass existing models in the context of 4-bit and 6-bit quantization.

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.

To bridge the ever increasing gap between deep neural networks' complexity and hardware capability, network quantization has attracted more and more research attention. The latest trend of mixed precision quantization takes advantage of hardware's multiple bit-width arithmetic operations to unleash the full potential of network quantization. However, this also results in a difficult integer programming formulation, and forces most existing approaches to use an extremely time-consuming search process even with various relaxations. Instead of solving a problem of the original integer programming, we propose to optimize a proxy metric, the concept of network orthogonality, which is highly correlated with the loss of the integer programming but also easy to optimize with linear programming. This approach reduces the search time and required data amount by orders of magnitude, with little compromise on quantization accuracy. Specifically, we achieve 72.08% Top-1 accuracy on ResNet-18 with 6.7Mb, which does not require any searching iterations. Given the high efficiency and low data dependency of our algorithm, we used it for the post-training quantization, which achieve 71.27% Top-1 accuracy on MobileNetV2 with only 1.5Mb. Our code is available at https://github.com/MAC-AutoML/OMPQ.

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments.

We study the challenging task of neural network quantization without end-to-end retraining, called Post-training Quantization (PTQ). PTQ usually requires a small subset of training data but produces less powerful quantized models than Quantization-Aware Training (QAT). In this work, we propose a novel PTQ framework, dubbed BRECQ, which pushes the limits of bitwidth in PTQ down to INT2 for the first time. BRECQ leverages the basic building blocks in neural networks and reconstructs them one-by-one. In a comprehensive theoretical study of the second-order error, we show that BRECQ achieves a good balance between cross-layer dependency and generalization error. To further employ the power of quantization, the mixed precision technique is incorporated in our framework by approximating the inter-layer and intra-layer sensitivity. Extensive experiments on various handcrafted and searched neural architectures are conducted for both image classification and object detection tasks. And for the first time we prove that, without bells and whistles, PTQ can attain 4-bit ResNet and MobileNetV2 comparable with QAT and enjoy 240 times faster production of quantized models. Codes are available at https://github.com/yhhhli/BRECQ.

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.

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.

Softmax attention stores key and value vectors for every preceding token, causing inference memory to grow with sequence length. Recent language models incorporating Gated DeltaNet (GDN) or Kimi Delta Attention (KDA) reduce this cost by replacing the KV cache in most layers with fixed-size recurrent states. However, these recurrent states are commonly stored in FP32 and consume substantial GPU memory; their updates are memory-bandwidth bound and contribute significantly to decoding latency. To our knowledge, we are the first to study post-training quantization of recurrent states in GDN and KDA based language models. We find that uniform quantization provides a poor accuracy--storage trade-off: INT8 and FP8 already degrade accuracy on complex reasoning tasks, while INT4 and NVFP4 reduce it to near zero. We further find that most quantization-error energy is concentrated in a small subset of channels and that the relative decay strength of state channels remains stable across prompts and tasks. Motivated by these findings, DAMP uses both quantization-error energy and decay-based persistence to identify high-risk channels during offline calibration. It stores these channels at higher precision and the remainder in INT8. We evaluate DAMP on Qwen3.6-35B and Kimi-Linear-48B across six benchmarks covering mathematical reasoning, general reasoning, and code generation. At 9.9 bits per state value, DAMP maintains average accuracy close to the FP32 baseline. DAMP reduces recurrent-state storage by 69.1%, accelerates the recurrent-state update kernel by up to 2.01x, and lowers full-model TPOT by up to 10.9%.

Vision-Language-Action models (VLAs) have demonstrated strong potential for embodied AI, yet their deployment on resource-limited robots remains challenging due to high memory and computational demands. While Post-Training Quantization (PTQ) provides an efficient solution, directly applying PTQ to VLAs often results in severe performance degradation during sequential control. We identify temporal error accumulation as a key factor, where quantization perturbations at the vision-language-to-action interface are progressively amplified, leading to kinematic drift in executed trajectories. To address this issue, we propose Drift-Aware Post-Training Quantization (DA-PTQ), which formulates quantization as a drift-aware optimization problem over sequential decision processes. DA-PTQ consists of two components: (1) Cross-Space Representation Compensation, which mitigates structured distortions between multimodal representations and action space to improve action consistency, and (2) Motion-Driven Mixed-Precision Allocation, which assigns bit-widths by minimizing trajectory-level motion errors. Extensive experiments show that DA-PTQ significantly reduces kinematic drift and achieves comparable performance to full-precision models under low-bit settings, enabling practical deployment of VLAs on resource-limited robotic platforms.

Recent generative models have become increasingly powerful, but their inference cost continues to grow. Model quantization offers a promising way to compress these models and accelerate inference. However, at 4 bits, activation quantization is substantially more challenging than weight quantization. Recent post-training quantization (PTQ) and quantization-aware training (QAT) methods have made progress in 4-bit activation quantization by introducing smoothing, SVD branches, rotations, mixed precision, or advanced formats such as NVFP4. These additional operators and data types impose demanding requirements on inference engines and hardware, limiting the broad adoption of low-precision models. Can quantization be achieved using only plain low-bit operators? To answer this question, we propose JustQuant, a simple yet effective framework that moves the complexity of low-bit quantization from deployment-time operators into the training process. We first revisit model quantization from the perspective of knowledge distillation and show that a key reason existing PTQ and QAT methods fail is that they typically exploit supervision at only a single level. We then introduce Theseus QAD, a quantization-aware distillation method that progressively applies multi-level supervision, analogous to the gradual replacement process in the Ship of Theseus. Extensive experiments on DiT and diffusion large language models show two distinct regimes. For smaller models, Theseus QAD can serve as a lightweight warm-up stage that substantially improves subsequent QAT with plain operators, while naive QAD may collapse in the same setting. For larger models, Theseus QAD provides a stronger distillation training path than ordinary QAD. Across both regimes, JustQuant improves low-bit quantization quality while avoiding the complex operators required by many existing PTQ methods.

We present OuroMamba, the first data-free post-training quantization (DFQ) method for vision Mamba-based models (VMMs). We identify two key challenges in enabling DFQ for VMMs, (1) VMM's recurrent state transitions restricts capturing of long-range interactions and leads to semantically weak synthetic data, (2) VMM activations exhibit dynamic outlier variations across time-steps, rendering existing static PTQ techniques ineffective. To address these challenges, OuroMamba presents a two-stage framework: (1) OuroMamba-Gen to generate semantically rich and meaningful synthetic data. It applies contrastive learning on patch level VMM features generated through neighborhood interactions in the latent state space, (2) OuroMamba-Quant to employ mixed-precision quantization with lightweight dynamic outlier detection during inference. In specific, we present a thresholding based outlier channel selection strategy for activations that gets updated every time-step. Extensive experiments across vision and generative tasks show that our data-free OuroMamba surpasses existing data-driven PTQ techniques, achieving state-of-the-art performance across diverse quantization settings. Additionally, we implement efficient GPU kernels to achieve practical latency speedup of up to 2.36x. Code and synthetic dataset are available here: https://github.com/georgia-tech-synergy-lab/ICCV-OuroMamba

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 .

Vision-Language-Action (VLA) models unify perception, reasoning, and control within a single policy, yet their multi-billion-parameter backbones and diffusion-based action heads make on-device deployment prohibitively expensive. Prior quantization efforts offer only partial solutions, compressing the LLM backbone while leaving the DiT action head at full precision, or resorting to mixed-precision schemes, driven by the belief that uniformly quantizing the action head is inherently unstable. We challenge this assumption with Omega-QVLA, the first training-free post-training quantization framework that compresses both the language backbone and the entire diffusion action head of a VLA model to a uniform W4A4 precision, eliminating the need for mixed-precision allocation. Omega-QVLA combines a composite SVD-Hadamard rotation that equalizes per-channel weight energy while diffusing residual activation outliers with per-step DiT activation scaling quantization that absorbs dynamic-range drift across denoising steps. On LIBERO, Omega-QVLA compresses Pi 0.5 and GR00T N1.5 to W4A4 with 98.0% and 87.8% task success rates, matching or exceeding their FP16 references of 97.1% and 87.0%, while reducing the static memory footprint by 71.3%. Real-world manipulation experiments further confirm smooth, accurate manipulation where prior methods fail. Code is available at https://github.com/UCMP13753/Omega-QVLA.

Deploying high-quality automatic speech recognition (ASR) on edge devices requires models that jointly optimize accuracy, latency, and memory footprint while operating entirely on CPU without GPU acceleration. We conduct a systematic empirical study of state-of-the-art ASR architectures, encompassing encoder-decoder, transducer, and LLM-based paradigms, evaluated across batch, chunked, and streaming inference modes. Through a comprehensive benchmark of over 50 configurations spanning OpenAI Whisper, NVIDIA Nemotron, Parakeet TDT, Canary, Conformer Transducer, and Qwen3-ASR, we identify NVIDIA's Nemotron Speech Streaming as the strongest candidate for real-time English streaming on resource-constrained hardware. We then re-implement the complete streaming inference pipeline in ONNX Runtime and conduct a controlled evaluation of multiple post-training quantization strategies, including importance-weighted k-quant, mixed-precision schemes, and round-to-nearest quantization, combined with graph-level operator fusion. These optimizations reduce the model from 2.47 GB to as little as 0.67 GB while maintaining word error rate (WER) within 1% absolute of the full-precision PyTorch baseline. Our recommended configuration, the int4 k-quant variant, achieves 8.20% average streaming WER across eight standard benchmarks, running comfortably faster than real-time on CPU with 0.56 s algorithmic latency, establishing a new quality-efficiency Pareto point for on-device streaming ASR.

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.

The complicated architecture and high training cost of vision transformers urge the exploration of post-training quantization. However, the heavy-tailed distribution of vision transformer activations hinders the effectiveness of previous post-training quantization methods, even with advanced quantizer designs. Instead of tuning the quantizer to better fit the complicated activation distribution, this paper proposes NoisyQuant, a quantizer-agnostic enhancement for the post-training activation quantization performance of vision transformers. We make a surprising theoretical discovery that for a given quantizer, adding a fixed Uniform noisy bias to the values being quantized can significantly reduce the quantization error under provable conditions. Building on the theoretical insight, NoisyQuant achieves the first success on actively altering the heavy-tailed activation distribution with additive noisy bias to fit a given quantizer. Extensive experiments show NoisyQuant largely improves the post-training quantization performance of vision transformer with minimal computation overhead. For instance, on linear uniform 6-bit activation quantization, NoisyQuant improves SOTA top-1 accuracy on ImageNet by up to 1.7%, 1.1% and 0.5% for ViT, DeiT, and Swin Transformer respectively, achieving on-par or even higher performance than previous nonlinear, mixed-precision quantization.

Large Language Models (LLMs) have greatly advanced the natural language processing paradigm. However, the high computational load and huge model sizes pose a grand challenge for deployment on edge devices. To this end, we propose APTQ (Attention-aware Post-Training Mixed-Precision Quantization) for LLMs, which considers not only the second-order information of each layer's weights, but also, for the first time, the nonlinear effect of attention outputs on the entire model. We leverage the Hessian trace as a sensitivity metric for mixed-precision quantization, ensuring an informed precision reduction that retains model performance. Experiments show APTQ surpasses previous quantization methods, achieving an average of 4 bit width a 5.22 perplexity nearly equivalent to full precision in the C4 dataset. In addition, APTQ attains state-of-the-art zero-shot accuracy of 68.24\% and 70.48\% at an average bitwidth of 3.8 in LLaMa-7B and LLaMa-13B, respectively, demonstrating its effectiveness to produce high-quality quantized LLMs.

Early wildfire detection in remote and forest areas is crucial for minimizing devastation and preserving ecosystems. Autonomous drones offer agile access to remote, challenging terrains, equipped with advanced imaging technology that delivers both high-temporal and detailed spatial resolution, making them valuable assets in the early detection and monitoring of wildfires. However, the limited computation and battery resources of Unmanned Aerial Vehicles (UAVs) pose significant challenges in implementing robust and efficient image classification models. Current works in this domain often operate offline, emphasizing the need for solutions that can perform inference in real time, given the constraints of UAVs. To address these challenges, this paper aims to develop a real-time image classification and fire segmentation model. It presents a comprehensive investigation into hardware acceleration using the Jetson Nano P3450 and the implications of TensorRT, NVIDIA's high-performance deep-learning inference library, on fire classification accuracy and speed. The study includes implementations of Quantization Aware Training (QAT), Automatic Mixed Precision (AMP), and post-training mechanisms, comparing them against the latest baselines for fire segmentation and classification. All experiments utilize the FLAME dataset - an image dataset collected by low-altitude drones during a prescribed forest fire. This work contributes to the ongoing efforts to enable real-time, on-board wildfire detection capabilities for UAVs, addressing speed and the computational and energy constraints of these crucial monitoring systems. The results show a 13% increase in classification speed compared to similar models without hardware optimization. Comparatively, loss and accuracy are within 1.225% of the original values.

Diffusion large language models (dLLMs), which offer bidirectional context and flexible masked-denoising generation, are emerging as a compelling alternative to autoregressive (AR) LLMs. However, like AR LLMs, their model sizes continue to grow, motivating weight compression for deployment. Although post-training quantization (PTQ) is effective for AR LLMs, directly transferring it to dLLMs at 2-bit leads to unsatisfactory performance. To tackle these challenges, we propose Quant-dLLM, an ultra-low-bit PTQ framework tailored to dLLMs. Since masked-denoising activations in dLLMs differ from the fully visible signals assumed by standard PTQ methods, we introduce Masked Calibration Simulation (MCS) to align calibration with the timestep-dependent masking, which yields more reliable calibrations. Moreover, we propose a Data-aware Any-order Quantizer (DAQ) that learns ultra-low-bit weight representations via an optimization algorithm. It performs iterative approximation guided by our simulated calibration data. In addition, under a strict 2-bit budget, we introduce Adaptive Blockwise Mixed Precision (ABMP), a sensitivity-based precision allocation scheme that adaptively assigns bit width across channel groups. When restricted to 2-bit precision, Quant-dLLM consistently achieves higher accuracy than state-of-the-art (SOTA) AR-transfer PTQ methods on dLLMs. The code and models will be available at: https://github.com/ZTA2785/Quant-dLLM.

An estimated 1 billion people worldwide live with vision impairment, yet current vision-language models (VLMs) produce descriptions too vague for safe navigation by blind and low-vision (BLV) users. Large VLMs can generate high-quality audio-description-compliant narrations but cannot run on mobile devices; small VLMs offer competitive latency but lack spatial detail, directional cues, and hazard awareness for navigational assistance. We present Smol-VL-BLV, a compact VLM for blind and low-vision users that closes this gap using a 500M decoder transformer model and two post-training mechanisms: (1) teacher-student distillation and (2) Group Relative Policy Optimization (GRPO) with a composite BLV reward targeting directional language, metric distances, and hazard detection. Because multi-stage post-training can induce catastrophic forgetting, we add a lightweight finetuning stage after the last stage GRPO finetuning to recover general descriptive quality while preserving BLV-specific spatial grounding. Our best model substantially outperforms the baseline across various benchmarks, including tasks: VQA, BLV captioning, OCR, and latency. Compared with the baseline for relative improvement, it improves the Spatial score gain of 19.3%, and the Social score gain of 14.8%. It also increases OCR-Bench by 101.5%, and raises TextVQA accuracy by 44.2%. These results show that BLV-focused post-training improves both accessibility-specific spatial grounding and general visual-text reasoning. Deployed on a mid-range Android smartphone via Mixed-Precision Quantization, the model remains approx. 450 MB and runs entirely on-device, offline and without network dependency, generating descriptions with latency dependent on host hardware capabilities. Our model, dataset, and code is publicly released at https://smol-vl-blv.github.io/Smol-VL-BLV-website/

To adopt convolutional neural networks (CNN) for a range of resource-constrained targets, it is necessary to compress the CNN models by performing quantization, whereby precision representation is converted to a lower bit representation. To overcome problems such as sensitivity of the training dataset, high computational requirements, and large time consumption, post-training quantization methods that do not require retraining have been proposed. In addition, to compensate for the accuracy drop without retraining, previous studies on post-training quantization have proposed several complementary methods: calibration, schemes, clipping, granularity, and mixed-precision. To generate a quantized model with minimal error, it is necessary to study all possible combinations of the methods because each of them is complementary and the CNN models have different characteristics. However, an exhaustive or a heuristic search is either too time-consuming or suboptimal. To overcome this challenge, we propose an auto-tuner known as Quantune, which builds a gradient tree boosting model to accelerate the search for the configurations of quantization and reduce the quantization error. We evaluate and compare Quantune with the random, grid, and genetic algorithms. The experimental results show that Quantune reduces the search time for quantization by approximately 36.5x with an accuracy loss of 0.07 ~ 0.65% across six CNN models, including the fragile ones (MobileNet, SqueezeNet, and ShuffleNet). To support multiple targets and adopt continuously evolving quantization works, Quantune is implemented on a full-fledged compiler for deep learning as an open-sourced project.

Large Language Models (LLMs) exhibit impressive performance across various tasks, but deploying them for inference poses challenges. Their high resource demands often necessitate complex, costly multi-GPU pipelines, or the use of smaller, less capable models. While quantization offers a promising solution utilizing lower precision for model storage, existing methods frequently experience significant performance drops at lower precision levels. Additionally, they typically provide only a limited set of solutions at specific bit levels, many of which are extensively manually tuned. To address these challenges, we propose a new method called SKIM: Scaled K-means clustering wIth Mixed precision. Our approach introduces two novel techniques: 1. A greedy algorithm to solve approximately optimal bit allocation across weight channels, and 2. A trainable scaling vector for non-differentiable K-means clustering. These techniques substantially improve performance and can be adapted to any given bit. Notably, in terms of model perplexity, our method narrows the gap between 3-bit quantized LLaMA models and their full precision counterparts by 16.3% on average.

Extreme low-bit quantization is critical for efficiently deploying Large Language Models (LLMs), yet it often leads to severe performance degradation at 2-bits and even 4-bits (e.g., MXFP4). We present SignRoundV2, a post-training quantization framework that is highly effective even without mixed-precision. SignRoundV2 introduces (1) a fast sensitivity metric that combines gradient information with quantization-induced deviations to guide layer-wise bit allocation, and (2) a lightweight pre-tuning search for quantization scales to improve extremely low-bit quantization. These components allow SignRoundV2 to close the gap with full-precision models. Extensive experiments indicate that our method sustains competitive accuracy for LLMs, achieving production-grade performance with about 1 percent variance at 4-5 bits and strong results even at 2 bits. The implementation is available at https://github.com/intel/auto-round.

Mixed-precision quantization has been widely applied on deep neural networks (DNNs) as it leads to significantly better efficiency-accuracy tradeoffs compared to uniform quantization. Meanwhile, determining the exact precision of each layer remains challenging. Previous attempts on bit-level regularization and pruning-based dynamic precision adjustment during training suffer from noisy gradients and unstable convergence. In this work, we propose Continuous Sparsification Quantization (CSQ), a bit-level training method to search for mixed-precision quantization schemes with improved stability. CSQ stabilizes the bit-level mixed-precision training process with a bi-level gradual continuous sparsification on both the bit values of the quantized weights and the bit selection in determining the quantization precision of each layer. The continuous sparsification scheme enables fully-differentiable training without gradient approximation while achieving an exact quantized model in the end.A budget-aware regularization of total model size enables the dynamic growth and pruning of each layer's precision towards a mixed-precision quantization scheme of the desired size. Extensive experiments show CSQ achieves better efficiency-accuracy tradeoff than previous methods on multiple models and datasets.

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.

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.

Mixed-Precision Quantization~(MQ) can achieve a competitive accuracy-complexity trade-off for models. Conventional training-based search methods require time-consuming candidate training to search optimized per-layer bit-width configurations in MQ. Recently, some training-free approaches have presented various MQ proxies and significantly improve search efficiency. However, the correlation between these proxies and quantization accuracy is poorly understood. To address the gap, we first build the MQ-Bench-101, which involves different bit configurations and quantization results. Then, we observe that the existing training-free proxies perform weak correlations on the MQ-Bench-101. To efficiently seek superior proxies, we develop an automatic search of proxies framework for MQ via evolving algorithms. In particular, we devise an elaborate search space involving the existing proxies and perform an evolution search to discover the best correlated MQ proxy. We proposed a diversity-prompting selection strategy and compatibility screening protocol to avoid premature convergence and improve search efficiency. In this way, our Evolving proxies for Mixed-precision Quantization~(EMQ) framework allows the auto-generation of proxies without heavy tuning and expert knowledge. Extensive experiments on ImageNet with various ResNet and MobileNet families demonstrate that our EMQ obtains superior performance than state-of-the-art mixed-precision methods at a significantly reduced cost. The code will be released.

The 8 bits quantization has been widely applied to accelerate network inference in various deep learning applications. There are two kinds of quantization methods, training-based quantization and post-training quantization. Training-based approach suffers from a cumbersome training process, while post-training quantization may lead to unacceptable accuracy drop. In this paper, we present an efficient and simple post-training method via scale optimization, named EasyQuant (EQ),that could obtain comparable accuracy with the training-based method.Specifically, we first alternately optimize scales of weights and activations for all layers target at convolutional outputs to further obtain the high quantization precision. Then, we lower down bit width to INT7 both for weights and activations, and adopt INT16 intermediate storage and integer Winograd convolution implementation to accelerate inference.Experimental results on various computer vision tasks show that EQ outperforms the TensorRT method and can achieve near INT8 accuracy in 7 bits width post-training.

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

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.

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

Quantization-aware training (QAT) leverages lower-precision arithmetic to reduce the cost of LLM deployment, but aggressive quantization degrades final model performance. A common remedy is mixed-precision training, in which high precision is assigned to some of the layers to maintain performance while keeping the cost constrained. This approach then requires precision assignments for model layers during training. We provide a new approach, called Q-PACE, consisting of a second-order sensitivity model that predicts the loss increase as a sum of quantization noise MSE weighted by per-layer curvature coefficients. During training, we periodically re-compute these coefficients using perturbations across layers, and re-assign precision. Pretraining and supervised fine-tuning experiments on LLMs of up to 4B parameters show that Q-PACE consistently improves over existing mixed-precision training recipes, and achieves comparable loss at substantially lower total memory budgets. We further find that quantization sensitivity is highly predictable by depth and layer type, and its stability during training allows for infrequent, cheap recalibration.

Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive discrete optimization to determine precision allocation, or introduce hardware inefficiencies due to irregular memory layouts. We propose SFMP, a search-free and hardware-friendly mixed-precision quantization framework for large language models. The framework is built upon four novel ideas: Fractional bit-width, which extends integer bit-width for weight matrix to fractional value and transforms discrete precision allocation as a continuous problem; 2)Block-wise mixed-precision, enabling fine-grained precision within weight matrices while remaining hardware-friendly; 3)Row-column weight reordering, which aggregates salient weights via row and column reordering, incurring only a small activation reordering overhead during inference; 4)Unified GEMM kernel, which supports mixed-precision GEMM at arbitrary average bit-width. Extensive experiments demonstrate that SFMP outperforms state-of-the-art layer-wise mixed-precision methods under the same memory constraints, while significantly reducing quantization cost and improving inference efficiency. Code is available at https://github.com/Nkniexin/SFMP

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.

Deploying deep learning models on edge CPUs is bottlenecked by computational and memory constraints. Mixed-precision quantization promises to reduce inference latency while preserving accuracy. However, quantization affects different layer types in inconsistent ways, so identifying where accuracy loss is minimized and latency reduction is maximized is critical, as the effect accumulates over a full deployment into substantial savings or unacceptable task degradation. Such identification relies on sensitivity metrics, proxies that estimate layer-wise degradation without evaluating the task accuracy of every candidate policy. Nevertheless, widely used metrics fail systematically on modern architectures. We present a systematic empirical study of 13 sensitivity metrics for layer-wise INT8 quantization across four distinctly different neural networks, and validate the resulting policies on two ARM64 platforms. Gradient-based sensitivity methods fail on 4 out of 8 model-hardware configurations and weight-based statistics on 2. In contrast, the Jensen-Shannon Divergence achieves zero catastrophic failures, reliably isolating the layers that cannot be safely quantized. A sensitivity metric alone does not define a policy, and the fixed thresholds typically used for that step are fragile over the highly skewed distributions of modern architectures. We address this with K-Means clustering, achieving near-lossless accuracy and a mean speed-up of 1.81times over the full-precision model. Finally, we reveal that excluding from quantization the layers whose speed-up is negligible, regardless of their sensitivity, can be counterproductive, as it induces computational graph fragmentation and disables operator fusion. Our results yield concrete allocation policies for practitioners and researchers deploying quantized vision models on heterogeneous edge CPUs, without GPU access or gradient computation.

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.

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

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.

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.

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.

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

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.

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.

Mixture-of-experts (MoE) language models activate only a few experts per token, yet all expert weights must be stored. Mixed-precision quantization reduces this storage cost by assigning higher bit-widths to sensitive experts and lower bit-widths to resilient ones, but expert rankings alone do not determine how strongly to weight their errors. To address this gap, we propose NatScale, a contrast-calibrated allocation framework for mixed-precision MoE quantization. It uses a model-specific power transformation to calibrate gradient-based expert weights to an information-theoretic contrast target while preserving rankings. We jointly evaluate each expert's gate, up and down configurations to estimate its output error. We then combine these errors and calibrated weights with an existing prior based on weight spectra, variance and precision decay to select configurations under a storage budget. Across three models, NatScale achieves the lowest native-to-quantized KL divergence and the highest top-token agreement in all nine settings against five allocation baselines. It also yields the lowest perplexity in seven settings. These findings highlight the importance of objective-aware precision allocation.

Mixed-precision quantization (MPQ) has become a key technique for deploying large language models under stringent memory and compute constraints. We first identify a phenomenon that we term the Perplexity Illusion: layers ranked as important by perplexity-based sensitivity show little rank correlation with those that are most influential for complex reasoning performance, with Kendall τapprox 0 in our analysis. We further reveal an Alignment-Diversity Tradeoff: using only target-task calibration data can degrade post-quantization performance, whereas incorporating general-domain data stabilizes sensitivity estimation and improves robustness across tasks. Based on these observations, we propose TASA (Task-Aware Sensitivity Analysis), a two-level framework that jointly optimizes calibration-data composition and mixed-precision bit allocation. Specifically, TASA searches for a calibration-data mixture using a training-free gradient-trace alignment criterion, and then aggregates perplexity and reasoning-oriented sensitivity signals to guide both inter-layer and intra-layer bit allocation. Experiments on LLaMA-3-8B and Qwen2.5-7B reveal a precision inversion: appropriately allocated 3.5-bit models can match or surpass less task-aware 4-bit baselines. At an average precision of 3.5 bits, TASA matches or outperforms several competitive 4-bit uniform baselines in aggregate accuracy, and improves over the strongest W3 baseline on GSM8K by more than 20 absolute points on LLaMA-3-8B. These results show that calibration-data composition substantially affects task-sensitive quantization, a factor underexplored in prior work.

Quantization-aware training (QAT) schemes have been shown to achieve near-full precision accuracy. They accomplish this by training a quantized model for multiple epochs. This is computationally expensive, mainly because of the full precision backward pass. On the other hand, post-training quantization (PTQ) schemes do not involve training and are therefore computationally cheap, but they usually result in a significant accuracy drop. We address these challenges by proposing EfQAT, which generalizes both schemes by optimizing only a subset of the parameters of a quantized model. EfQAT starts by applying a PTQ scheme to a pre-trained model and only updates the most critical network parameters while freezing the rest, accelerating the backward pass. We demonstrate the effectiveness of EfQAT on various CNNs and Transformer-based models using different GPUs. Specifically, we show that EfQAT is significantly more accurate than PTQ with little extra compute. Furthermore, EfQAT can accelerate the QAT backward pass between 1.44-1.64x while retaining most accuracy.

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.

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.

Post-training quantization is widely used for compressing large neural networks, but aggressive low-bit quantization can significantly degrade model quality. A common remedy is to augment the quantized weights with a low-rank correction, leading to approximations of the form Wapprox Q+LR. In this paper, we study this low-precision plus low-rank representation through the layer-wise reconstruction objective |XW-X(Q+LR)|_F^2, where X is a calibration matrix. We establish, to our knowledge, the first information-theoretic lower bounds for this problem under finite-alphabet and bounded low-rank compensation constraints. We then propose GPTQ-intrinsic LoRA, a training-free algorithm that incorporates the low-rank correction directly into a GPTQ-style quantization pass by appropriately augmenting the calibration Hessian. For the choice L=V_r, where V_r contains the top right singular vectors of X, we prove layer-wise reconstruction error bounds in which the usual GPTQ dependence on |X|_F^2 is replaced by the rank-r residual |X-X_r|_F^2, up to regularization terms. Under natural structural assumptions, these bounds match the information-theoretic lower bounds in their dominant scaling, up to constants and mild factors. We also introduce Bid-Up, a fixed-grid quantization refinement step that can be alternated with optimal low-rank compensation with guaranteed non-increasing layer-wise reconstruction error. Experiments on Qwen3 language models and DeiT vision transformers show that GPTQ-intrinsic LoRA improves over GPTQ and GPTQ followed by low-rank compensation, with additional gains from refinement loops.

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.

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.

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

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.

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.

The burgeoning computational demands for training large language models (LLMs) necessitate efficient methods, including quantized training, which leverages low-bit arithmetic operations to reduce costs. While FP8 precision has shown potential, leveraging FP4 remains challenging due to inherent quantization errors and limited representation capability. Based on the Transformer architecture, we present an FP4 training scheme for LLMs, overcoming these obstacles through mixed-precision quantization strategies tailed for different modules and training stages. This allows us to apply the precision level suitable to distinct components within the model, ensuring that multi-head attention and linear layers are handled appropriately. Our pretraining recipe ensures stability in backpropagation by incorporating fine-grained quantization methods with a target precision training schedule. Experimental results demonstrate that our FP4 training scheme achieves accuracy comparable to BF16 and FP8, with smaller theoretical computational cost. With the advent of next-generation hardware supporting FP4, our method sets the foundation for efficient ultra-low precision training.

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.

This paper presents a novel mixed-precision quantization approach for speech foundation models that tightly integrates mixed-precision learning and quantized model parameter estimation into one single model compression stage. Experiments conducted on LibriSpeech dataset with fine-tuned wav2vec2.0-base and HuBERT-large models suggest the resulting mixed-precision quantized models increased the lossless compression ratio by factors up to 1.7x and 1.9x over the respective uniform-precision and two-stage mixed-precision quantized baselines that perform precision learning and model parameters quantization in separate and disjointed stages, while incurring no statistically word error rate (WER) increase over the 32-bit full-precision models. The system compression time of wav2vec2.0-base and HuBERT-large models is reduced by up to 1.9 and 1.5 times over the two-stage mixed-precision baselines, while both produce lower WERs. The best-performing 3.5-bit mixed-precision quantized HuBERT-large model produces a lossless compression ratio of 8.6x over the 32-bit full-precision system.

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.

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.

Post-training quantization (PTQ) reduces the memory footprint of LLMs by quantizing their weights to low-precision. In this work, we introduce QuIP#, a weight-only PTQ method that achieves state-of-the-art results in extreme compression regimes (le 4 bits per weight) using three novel techniques. First, QuIP# improves the incoherence processing from QuIP by using the randomized Hadamard transform, which is faster and has better theoretical properties. Second, QuIP# uses vector quantization techniques to take advantage of the ball-shaped sub-Gaussian distribution that incoherent weights possess: specifically, we introduce a set of hardware-efficient codebooks based on the highly symmetric E_8 lattice, which achieves the optimal 8-dimension unit ball packing. Third, QuIP# uses fine-tuning to improve fidelity to the original model. Our experiments show that QuIP# outperforms existing PTQ methods, enables new behaviors in PTQ scaling, and supports fast inference.

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

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.

Large language models (LLMs) have achieved impressive performance across various domains. However, the substantial hardware resources required for their training present a significant barrier to efficiency and scalability. To mitigate this challenge, low-precision training techniques have been widely adopted, leading to notable advancements in training efficiency. Despite these gains, low-precision training involves several componentsx2013such as weights, activations, and gradientsx2013each of which can be represented in different numerical formats. The resulting diversity has created a fragmented landscape in low-precision training research, making it difficult for researchers to gain a unified overview of the field. This survey provides a comprehensive review of existing low-precision training methods. To systematically organize these approaches, we categorize them into three primary groups based on their underlying numerical formats, which is a key factor influencing hardware compatibility, computational efficiency, and ease of reference for readers. The categories are: (1) fixed-point and integer-based methods, (2) floating-point-based methods, and (3) customized format-based methods. Additionally, we discuss quantization-aware training approaches, which share key similarities with low-precision training during forward propagation. Finally, we highlight several promising research directions to advance this field. A collection of papers discussed in this survey is provided in https://github.com/Hao840/Awesome-Low-Precision-Training.

Training LLMs at ultra-low precision remains a formidable challenge. Direct low-bit QAT often suffers from convergence instability and substantial training costs, exacerbated by quantization noise from heavy-tailed outlier channels and error accumulation across layers. To address these issues, we present Bit-by-Bit, a progressive QAT framework with outlier channel splitting. Our approach integrates three key components: (1) block-wise progressive training that reduces precision stage by stage, ensuring stable initialization for low-bit optimization; (2) nested structure of integer quantization grids to enable a "train once, deploy any precision" paradigm, allowing a single model to support multiple bit-widths without retraining; (3) rounding-aware outlier channel splitting, which mitigates quantization error while acting as an identity transform that preserves the quantized outputs. Furthermore, we follow microscaling groups with E4M3 scales, capturing dynamic activation ranges in alignment with OCP/NVIDIA standards. To address the lack of efficient 2-bit kernels, we developed custom operators for both W2A2 and W2A16 configurations, achieving up to 11times speedup over BF16. Under W2A2 settings, Bit-by-Bit significantly outperforms baselines like BitDistiller and EfficientQAT on both Llama2/3, achieving a loss of only 2.25 WikiText2 PPL compared to full-precision models.

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.

When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. We find that, perhaps surprisingly, this is not the best we can do. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. AdaRound is fast, does not require fine-tuning of the network, and only uses a small amount of unlabelled data. We start by theoretically analyzing the rounding problem for a pre-trained neural network. By approximating the task loss with a Taylor series expansion, the rounding task is posed as a quadratic unconstrained binary optimization problem. We simplify this to a layer-wise local loss and propose to optimize this loss with a soft relaxation. AdaRound not only outperforms rounding-to-nearest by a significant margin but also establishes a new state-of-the-art for post-training quantization on several networks and tasks. Without fine-tuning, we can quantize the weights of Resnet18 and Resnet50 to 4 bits while staying within an accuracy loss of 1%.

Deploying neural networks on microcontroller units (MCUs) presents substantial challenges due to their constrained computation and memory resources. Previous researches have explored patch-based inference as a strategy to conserve memory without sacrificing model accuracy. However, this technique suffers from severe redundant computation overhead, leading to a substantial increase in execution latency. A feasible solution to address this issue is mixed-precision quantization, but it faces the challenges of accuracy degradation and a time-consuming search time. In this paper, we propose QuantMCU, a novel patch-based inference method that utilizes value-driven mixed-precision quantization to reduce redundant computation. We first utilize value-driven patch classification (VDPC) to maintain the model accuracy. VDPC classifies patches into two classes based on whether they contain outlier values. For patches containing outlier values, we apply 8-bit quantization to the feature maps on the dataflow branches that follow. In addition, for patches without outlier values, we utilize value-driven quantization search (VDQS) on the feature maps of their following dataflow branches to reduce search time. Specifically, VDQS introduces a novel quantization search metric that takes into account both computation and accuracy, and it employs entropy as an accuracy representation to avoid additional training. VDQS also adopts an iterative approach to determine the bitwidth of each feature map to further accelerate the search process. Experimental results on real-world MCU devices show that QuantMCU can reduce computation by 2.2x on average while maintaining comparable model accuracy compared to the state-of-the-art patch-based inference methods.

Mixture-of-Experts (MoE) large language models incur substantial memory costs due to their large expert parameter counts. Mixed-precision quantization reduces these costs by allocating different bit-widths to experts or linear blocks according to their importance. However, assigning a single precision within each expert or linear block overlooks its internal structural heterogeneity. This limitation motivates two key questions: (1) how to define a fine-grained unit for quantization within a linear transformation; and (2) how to characterize the quantization cost of each unit under actual activation patterns and different bit-widths. To address these two questions, we propose BitsMoE, a cost-aware mixed-precision quantization framework built on two complementary techniques: (1) Shared-basis Spectral Decomposition (SSD) separates expert weights into a shared basis and expert-specific spectral components, defining structural quantization units while exploiting cross-expert redundancy. (2) Factorized Quantization Cost Modeling (FQCM) estimates component-wise costs from output reconstruction loss by combining intrinsic spectral importance, activation-dependent importance, and bit-width-dependent distortion. Using these component-wise costs, we formulate bit allocation as an integer linear program (ILP) that minimizes total modeled quantization cost under a fixed memory budget. On Qwen3-30B-A3B at 2-bit, BitsMoE achieves 64.29% average accuracy over seven downstream tasks, outperforming the evaluated MoE-specific methods, including those using ILP-based bit allocation, and exceeding GEMQ by 2.80 percentage points. Under the same setting, it achieves a 16.47times end-to-end offline quantization speedup over GEMQ. It also achieves up to 6.46times the decode throughput of GPTQ.

Current low-precision quantization algorithms often have the hidden cost of conversion back and forth from floating point to quantized integer values. This hidden cost limits the latency improvement realized by quantizing Neural Networks. To address this, we present HAWQV3, a novel mixed-precision integer-only quantization framework. The contributions of HAWQV3 are the following: (i) An integer-only inference where the entire computational graph is performed only with integer multiplication, addition, and bit shifting, without any floating point operations or even integer division; (ii) A novel hardware-aware mixed-precision quantization method where the bit-precision is calculated by solving an integer linear programming problem that balances the trade-off between model perturbation and other constraints, e.g., memory footprint and latency; (iii) Direct hardware deployment and open source contribution for 4-bit uniform/mixed-precision quantization in TVM, achieving an average speed up of 1.45times for uniform 4-bit, as compared to uniform 8-bit for ResNet50 on T4 GPUs; and (iv) extensive evaluation of the proposed methods on ResNet18/50 and InceptionV3, for various model compression levels with/without mixed precision. For ResNet50, our INT8 quantization achieves an accuracy of 77.58%, which is 2.68% higher than prior integer-only work, and our mixed-precision INT4/8 quantization can reduce INT8 latency by 23% and still achieve 76.73% accuracy. Our framework and the TVM implementation have been open sourced.

Diffusion Language Models (DLMs) introduce unique quantization challenges due to their iterative denoising process. In this work, we reveal that quantization sensitivity is both taskand time-dependent, with different downstream tasks exhibiting distinct precision requirements across denoising steps. We further show that these patterns can be predicted without groundtruth labels or task-specific evaluation metrics. Building on these findings, we introduce T 2Quant, a task and time-aware mixedprecision quantization framework that uses a label-free sensitivity signal to optimally allocate activation precision across denoising steps under a fixed bit-width budget. Extensive experiments across three DLMs and six benchmarks demonstrate that T 2Quant consistently improves the average accuracy of existing quantization methods, achieving gains of up to 6.7 percentage points under the same budget.

Post-training quantization reduces the deployment cost of large language models, yet how severely a quantized model degrades is not determined by bit-width alone. We systematically study weight-only post-training quantization across bit-widths, quantization methods, model scales and downstream tasks on multiple model families. We observe that such degradation varies substantially across these factors: 4-bit quantization usually preserves performance, 2-bit often causes broad degradation, and at 3-bit, degradation becomes apparent but varies markedly with task type, quantization method and model scale. To explain this variability, we use the signal-to-noise ratio (SNR) to measure how strongly quantization perturbs full-precision representations. We trace degradation back to two linked processes: how quantization errors arise within individual modules, and how they accumulate across layers. First, a source SNR decomposition shows that newly introduced errors depend on three factors: the magnitude of the weight error, the strength of the task-specific signal, and how strongly the quantization error aligns with task-specific activations. Different factors affect these components in distinct ways. Second, a cross-layer propagation analysis shows that these errors can be attenuated, preserved, or amplified as they pass across layers, and that larger models benefit from weaker error amplification. Together, these results establish that quantization degradation is governed by how errors are introduced at the source and how they accumulate across the network.

Post-training quantization (PTQ) is a widely used method to compress large language models (LLMs) without fine-tuning. It typically sets quantization hyperparameters (e.g., scaling factors) based on current-layer activations. Although this method is efficient, it suffers from quantization bias and error accumulation, resulting in suboptimal and unstable quantization, especially when the calibration data is biased. To overcome these issues, we propose Future-Aware Quantization (FAQ), which leverages future-layer activations to guide quantization. This allows better identification and preservation of important weights, while reducing sensitivity to calibration noise. We further introduce a window-wise preview mechanism to softly aggregate multiple future-layer activations, mitigating over-reliance on any single layer. To avoid expensive greedy search, we use a pre-searched configuration to minimize overhead. Experiments show that FAQ consistently outperforms prior methods with negligible extra cost, requiring no backward passes, data reconstruction, or tuning, making it well-suited for edge deployment.

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.

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

Training neural networks requires significant computational resources and energy. Methods like mixed-precision and quantization-aware training reduce bit usage, yet they still depend heavily on computationally expensive gradient-based optimization. In this work, we propose a paradigm shift: eliminate gradients altogether. One might hope that, in a finite quantized space, finding optimal weights with out gradients would be easier but we theoretically prove that this problem is NP-hard even in simple settings where the continuous case is efficiently solvable. To address this, we introduce a novel heuristic optimization framework that avoids full weight updates and significantly improves efficiency. Empirically, our method achieves performance comparable to that of full-precision gradient-based training on standard datasets and architectures, while using up to 3x less energy and requiring up to 5x fewer parameter updates.

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

Serving Large Language Models (LLMs) is costly. However, post-training weight quantization can address this problem by both compressing their sizes for limited memory and saving bandwidth for acceleration. As not all weight dimensions are equally important, those methods typically rely on a sensitivity metric, which indicates the element-wise influence of weights on loss function and is used to preprocess original weights for better quantization. In this work, we conduct an empirical study on the accuracy of the sensitivity metric, and find that existing gradient and Hessian based metrics are very inaccurate: they underestimate quantization's impact on the loss function by orders of magnitude, mainly due to the small convergence radius of local 2nd order approximation, \ie, gradient and Hessian term in Taylor's formula. To tackle this problem, we propose Post-quantization Integral (PQI), an accurate metric to estimate posterior sensitivity in a fine-grained manner. To leverage this accurate metric, we further propose ReQuant, a simple yet powerful framework that mainly consists of two Dense-and-Sparse detach components: self-adaptive outlier selection and step-wise significant weights detach. Results show that ReQuant boosts state-of-the-art post-training quantization methods, with a pronounced improvement of 2.66 perplexity gain on Llama 3.2 1B with QTIP.

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.

Large Language Models (LLMs) are widely used across many domains, but their scale makes deployment challenging. Post-Training Quantization (PTQ) reduces memory footprint without retraining by leveraging a small calibration set. Recent Hessian-based PTQ methods compensate quantization error via cross-channel dependencies, but such approaches degrade at low bit-widths due to noisy curvature estimates from limited calibration data. We propose DASH-Q, a robust PTQ framework using diagonal Hessian approximation and iterative weighted least squares. By discarding noise-prone dependencies, DASH-Q filters sampling noise while prioritizing the preservation of salient feature power. We outperform other PTQ baselines in ultra low-bit regime, improving zero-shot accuracy by 7.01% on average and up to 14.01% over the strongest baselines across five baseline LLM models, while showing robust and stable performance with very small calibration data.

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.

Post-training quantization is a key technique for reducing the memory and inference latency of large language models by quantizing weights and activations without requiring retraining. However, existing methods either (1) fail to account for the varying importance of hidden features to the end loss or, when incorporating end loss, (2) neglect the critical interactions between model weights. To address these limitations, we propose GuidedQuant, a novel quantization approach that integrates gradient information from the end loss into the quantization objective while preserving cross-weight dependencies within output channels. GuidedQuant consistently boosts the performance of state-of-the-art quantization methods across weight-only scalar, weight-only vector, and weight-and-activation quantization. Additionally, we introduce a novel non-uniform scalar quantization algorithm, which is guaranteed to monotonically decrease the quantization objective value, and outperforms existing methods in this category. We release the code at https://github.com/snu-mllab/GuidedQuant.

Post-training quantization (PTQ) is the go-to compression technique for large generative models, such as stable diffusion or large language models. PTQ methods commonly keep the softmax activation in higher precision as it has been shown to be very sensitive to quantization noise. However, this can lead to a significant runtime and power overhead during inference on resource-constraint edge devices. In this work, we investigate the source of the softmax sensitivity to quantization and show that the quantization operation leads to a large bias in the softmax output, causing accuracy degradation. To overcome this issue, we propose an offline bias correction technique that improves the quantizability of softmax without additional compute during deployment, as it can be readily absorbed into the quantization parameters. We demonstrate the effectiveness of our method on stable diffusion v1.5 and 125M-size OPT language model, achieving significant accuracy improvement for 8-bit quantized softmax.

Post-training quantization of Large Language Models (LLMs) has proven effective in reducing the computational requirements for running inference on these models. In this study, we focus on a straightforward question: When aiming for a specific accuracy or perplexity target for low-precision quantization, how many high-precision numbers or calculations are required to preserve as we scale LLMs to larger sizes? We first introduce a critical metric named the quantization ratio, which compares the number of parameters quantized to low-precision arithmetic against the total parameter count. Through extensive and carefully controlled experiments across different model families, arithmetic types, and quantization granularities (e.g. layer-wise, matmul-wise), we identify two central phenomenons. 1) The larger the models, the better they can preserve performance with an increased quantization ratio, as measured by perplexity in pre-training tasks or accuracy in downstream tasks. 2) The finer the granularity of mixed-precision quantization (e.g., matmul-wise), the more the model can increase the quantization ratio. We believe these observed phenomena offer valuable insights for future AI hardware design and the development of advanced Efficient AI algorithms.

Recent advancement in Automatic Speech Recognition (ASR) has produced large AI models, which become impractical for deployment in mobile devices. Model quantization is effective to produce compressed general-purpose models, however such models may only be deployed to a restricted sub-domain of interest. We show that ASR models can be personalized during quantization while relying on just a small set of unlabelled samples from the target domain. To this end, we propose myQASR, a mixed-precision quantization method that generates tailored quantization schemes for diverse users under any memory requirement with no fine-tuning. myQASR automatically evaluates the quantization sensitivity of network layers by analysing the full-precision activation values. We are then able to generate a personalised mixed-precision quantization scheme for any pre-determined memory budget. Results for large-scale ASR models show how myQASR improves performance for specific genders, languages, and speakers.

Ever-growing scale of large language models (LLMs) is pushing for improved efficiency, favoring fully quantized training (FQT) over BF16. While FQT accelerates training, it faces consistency challenges and requires searching over an exponential number of cases, each needing over 200B tokens to ensure stability. Pseudo-quantization training (PQT) addresses the issues of FQT, although it is not well-studied. We explore the practical implications of PQT in detail and propose a noise distribution R that is floating-point (FP)-friendly, with ideal properties including stochastic precision annealing. As a result, the proposed method serves as an effective theoretical foundation for low-precision FP parameters through PQT, utilizing efficient fake quantization via an addition and subsequent FP casting. We demonstrate that Gaussian weight sampling is (1) scalable: supports low-precision FP parameters down to FP6 and high-precision noise up to 9-bit with BF16 operator. The proposed method is (2) efficient: incurring computational overhead as low as 1.40\% on the A100 GPU in terms of Llama2 training tokens per second, and requiring 2 bytes per parameter in GPU memory. We demonstrate that PQT with Gaussian weight sampling is (3) stable: closely following or even surpassing performance of the BF16 baseline while pre-training GPT2 and Llama2 models with up to 1B parameters and 300B tokens.

Improving the efficiency of inference in Large Language Models (LLMs) is a critical area of research. Post-training Quantization (PTQ) is a popular technique, but it often faces challenges at low-bit levels, particularly in downstream tasks. Quantization-aware Training (QAT) can alleviate this problem, but it requires significantly more computational resources. To tackle this, we introduced Weight-Decomposed Low-Rank Quantization-Aware Training (DL-QAT), which merges the advantages of QAT while training only less than 1% of the total parameters. Specifically, we introduce a group-specific quantization magnitude to adjust the overall scale of each quantization group. Within each quantization group, we use LoRA matrices to update the weight size and direction in the quantization space. We validated the effectiveness of our method on the LLaMA and LLaMA2 model families. The results show significant improvements over our baseline method across different quantization granularities. For instance, for LLaMA-7B, our approach outperforms the previous state-of-the-art method by 4.2% in MMLU on 3-bit LLaMA-7B model. Additionally, our quantization results on pre-trained models also surpass previous QAT methods, demonstrating the superior performance and efficiency of our approach.

Quantization-Aware Training (QAT) integrates quantization into the training loop, enabling LLMs to learn robust low-bit representations, and is widely recognized as one of the most promising research directions. All current QAT research focuses on minimizing quantization error on full-precision models, where the full-precision accuracy acts as an upper bound (accuracy ceiling). No existing method has even attempted to surpass this ceiling. To break this ceiling, we propose a new paradigm: raising the ceiling (full-precision model), and then still quantizing it efficiently into 2 bits. We propose Fairypm i, the first 2-bit quantization framework for complex-valued LLMs. Specifically, our method leverages the representational advantages of the complex domain to boost full-precision accuracy. We map weights to the fourth roots of unity {pm1, pm i}, forming a perfectly symmetric and information-theoretically optimal 2-bit representation. Importantly, each quantized weight has either a zero real or imaginary part, enabling multiplication-free inference using only additions and element swaps. Experimental results show that Fairypm i outperforms the ceiling of existing 2-bit quantization approaches in terms of both PPL and downstream tasks, while maintaining strict storage and compute efficiency. This work opens a new direction for building highly accurate and practical LLMs under extremely low-bit constraints.

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

Post-training quantization (PTQ) is widely used to reduce the cost of serving large language models (LLMs), but its accuracy cost is uneven and is often tuned per model. We study where quantization damage occurs and how to allocate a small additional precision budget. Using causal mixed-precision intervention as ground truth (raise each layer to 8-bit in turn and measure the accuracy it recovers) across 9 open-weight models in 4 architecture families, we test 3 intuitive hypotheses: that quantization damage lives in task circuits, where the model computes, or in weight statistics. None of them predicts which layers benefit from restored precision. Recovery is instead diffuse: for 8 of 9 models, recovering 75% of the gap takes roughly half the layers; the lone exception, Qwen3-8B, is sharply concentrated. At a matched precision budget, spending it globally on finer quantization granularity beats locally repairing the most recoverable layers for all 8 group-128-compatible models (all but OpenLLaMA, whose width rules out group-128), by 21-52 points, including the concentrated Qwen3-8B. We report 2 secondary findings: the residual is budget-limited (8-bit is near-lossless in our evaluation across RTN, GPTQ, and AWQ), and the location of peak recovery correlates with architecture within a family, though not across families. Within this budget setting, global granularity is a better default than selectively protecting critical layers. More broadly, cheap signals that correlate with quantization damage do not necessarily identify where restoring precision improves accuracy; this must be tested with causal intervention.

Deploying transformer-based neural networks on resource-constrained edge devices presents a significant challenge. This challenge is often addressed through various techniques, such as low-rank approximation and mixed-precision quantization. In this work, we introduce Mixed Low-Rank and Quantization (MLoRQ), a novel method that integrates both techniques. MLoRQ employs a two-stage optimization process to determine optimal bit-width and rank assignments for each layer, adhering to predefined memory constraints. This process includes: (i) an intra-layer optimization that identifies potentially optimal compression solutions out of all low-rank and quantization combinations; (ii) an inter-layer optimization that assigns bit-width precision and rank to each layer while ensuring the memory constraint is met. An optional final step applies a sequential optimization process using a modified adaptive rounding technique to mitigate compression-induced errors in joint low-rank approximation and quantization. The method is compatible and can be seamlessly integrated with most existing quantization algorithms. MLoRQ shows state-of-the-art results with up to 15\% performance improvement, evaluated on Vision Transformers for image classification, object detection, and instance segmentation tasks.

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93\% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2\% of pairs. We propose the coverage model f(S)=cbigl(1-prod_{iin S}(1-a_i)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

Mixture-of-Experts (MoE) architectures scale model capacity through sparse expert activation, but their deployment remains memory-bound because all expert weights must reside in memory. Mixed-precision quantization can substantially reduce this footprint by assigning different bit-widths to different experts. Existing approaches, however, typically rely on calibration data to estimate expert importance and determine bit allocation. For frontier MoE LLMs, the original training data, and hence the true training distribution, is proprietary and inaccessible. As a result, calibration sets are inevitably imperfect surrogates, and this can misestimate expert utilization and lead to suboptimal bit allocation. Motivated by the substantial cross-expert quality variability observed in modern MoE models, and by the success of Heavy-Tailed Self-Regularization (HT-SR) theory at predicting neural network model quality without access to training or testing data, we propose AlphaQ, a calibration-free bit-allocation method for MoE quantization. AlphaQ draws on HT-SR theory and follows a simple principle: experts with more heavy-tailed weight spectra are typically better trained and hence should receive higher bit-widths, while experts with weaker heavy-tailed structure can be quantized more aggressively. AlphaQ operationalizes this principle by measuring expert-wise spectral heavy-tailedness and solving a budget-constrained optimization problem that minimizes total quantization error under a global bit-budget constraint. Across several MoE models, AlphaQ consistently outperforms calibration-based baselines under matched bit budgets. Notably, on Qwen1.5-MoE, AlphaQ achieves near full-precision accuracy with an average expert precision of only 3.5 bits, while delivering more than 4times memory compression. Our code is available at https://github.com/Superone77/AlphaQ.

Large language models (LLMs) have transformed natural-language processing, yet their scale makes real-world deployment costly. Post-training quantization reduces memory and computation but often degrades accuracy, while quantization-aware training can recover performance at the cost of extra training. Pushing quantization to the ternary (2-bit) regime yields even larger savings but is notoriously unstable. Building on recent work showing that a bias-free, RMS-normalized Transformer with straight-through estimation can reach 1.58-bit precision, we demonstrate that simply inserting RMS normalization before every linear projection and applying a gradual, layer-wise quantization schedule stably fine-tunes full-precision checkpoints into ternary LLMs. Our approach matches or surpasses more elaborate knowledge-distillation pipelines on standard language-modeling benchmarks without adding model complexity. These results indicate that careful normalization alone can close much of the accuracy gap between ternary and full-precision LLMs, making ultra-low-bit inference practical.

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.

The growing computational demands of training large language models (LLMs) necessitate more efficient methods. Quantized training presents a promising solution by enabling low-bit arithmetic operations to reduce these costs. While FP8 precision has demonstrated feasibility, leveraging FP4 remains a challenge due to significant quantization errors and limited representational capacity. This work introduces the first FP4 training framework for LLMs, addressing these challenges with two key innovations: a differentiable quantization estimator for precise weight updates and an outlier clamping and compensation strategy to prevent activation collapse. To ensure stability, the framework integrates a mixed-precision training scheme and vector-wise quantization. Experimental results demonstrate that our FP4 framework achieves accuracy comparable to BF16 and FP8, with minimal degradation, scaling effectively to 13B-parameter LLMs trained on up to 100B tokens. With the emergence of next-generation hardware supporting FP4, our framework sets a foundation for efficient ultra-low precision training.

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.

We consider the problem of accurate quantization for language models, where both the weights and activations are uniformly quantized to 4 bits per parameter, the lowest bitwidth format natively supported by GPU hardware. In this context, the key challenge is activation quantization: it is known that language models contain outlier channels whose values on average are orders of magnitude higher than than other channels, which prevents accurate low-bitwidth quantization with known techniques. We systematically study this phenomena and find that these outlier channels emerge early in training, and that they occur more frequently in layers with residual streams. We then propose a simple strategy which regularizes a layer's inputs via quantization-aware training (QAT) and its outputs via activation kurtosis regularization. We show that regularizing both the inputs and outputs is crucial for preventing a model's "migrating" the difficulty in input quantization to the weights, which makes post-training quantization (PTQ) of weights more difficult. When combined with weight PTQ, we show that our approach can obtain a W4A4 model that performs competitively to the standard-precision W16A16 baseline.

Quantization is a technique for reducing deep neural networks (DNNs) training and inference times, which is crucial for training in resource constrained environments or applications where inference is time critical. State-of-the-art (SOTA) quantization approaches focus on post-training quantization, i.e., quantization of pre-trained DNNs for speeding up inference. While work on quantized training exists, most approaches require refinement in full precision (usually single precision) in the final training phase or enforce a global word length across the entire DNN. This leads to suboptimal assignments of bit-widths to layers and, consequently, suboptimal resource usage. In an attempt to overcome such limitations, we introduce AdaPT, a new fixed-point quantized sparsifying training strategy. AdaPT decides about precision switches between training epochs based on information theoretic conditions. The goal is to determine on a per-layer basis the lowest precision that causes no quantization-induced information loss while keeping the precision high enough such that future learning steps do not suffer from vanishing gradients. The benefits of the resulting fully quantized DNN are evaluated based on an analytical performance model which we develop. We illustrate that an average speedup of 1.27 compared to standard training in float32 with an average accuracy increase of 0.98% can be achieved for AlexNet/ResNet on CIFAR10/100 and we further demonstrate these AdaPT trained models achieve an average inference speedup of 2.33 with a model size reduction of 0.52.

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.

Post-training model quantization is a widely adopted technique for reducing the memory and computational costs of large language models (LLMs). However, most existing methods rely on uniform or heuristic bitwidth assignments, failing to account for the nonuniform sensitivity of weights to quantization noise. In this paper, we propose a novel framework for allocating quantization bitwidths based on sensitivity metrics derived from a Hessian proxy. We make key assumptions, which allow the layer/component-wise loss function to be expressed as an explicit function of the bitwidths. This enables a neat formulation of the bit allocation problem as a convex optimization task, whose closed-form solution adapts precision across weights to minimize the layer-wise quantization loss. Inspecting the solution provides several insights (such as the equal-loss structure), which are then exploited to design the proposed BAQ (Bit Allocation Quantization) algorithm. The proposed algorithm achieves a good trade-off between loss minimization and complexity and allows BAQ to be integrated into standard quantization pipelines with minimal overhead. Experimental results show that BAQ consistently outperforms GPTQ, achieving up to 56times lower perplexity at the same bitwidth on large language models ranging from 125M to 30B parameters. Leveraging our analytical results derived from solving the optimal bit allocation problem, we also provide a theoretical explanation for the observed gains. All codes of this paper are available at https://github.com/CSU-ModelCompression/BAQ.

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.

Multimodal large language models (MLLMs) require huge memory and computational costs, which limits their practical deployment. Post-training quantization (PTQ) techniques offer an efficient solution for model compression and inference acceleration. Yet, the quantized model faces performance degradation due to outlier channels, which are highly sensitive to quantization and substantially impair activation fidelity and task accuracy. To protect these salient channels during quantization, existing PTQ methods leverage modality- or token-level metrics to guide channel-wise scaling (CWS) of LLM decoders. However, these orthogonal measurements fail to capture channel-wise impacts on task-specific loss, and the misalignment between importance and scaling factors ultimately leads to suboptimal performance. To address this issue, we propose C-PTQ, a unified channel-wise PTQ method that harmonizes task-specific loss perturbation and quantization error. Motivated by second-order derivatives, we design a Fisher-weighted objective as a tractable Hessian approximation, seamlessly injecting task sensitivity into the scaling process. Notably, we achieve state-of-the-art performance without auxiliary modules like LoRA, thereby maintaining high efficiency. Experiments on Qwen2.5VL, InternVL2 and LLaVA-OV across 8 benchmarks demonstrate our effectiveness in both weight-only and weight-activation settings.