LLM Quantization

LLM: Large Language Model

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Overview

LLM quantization studies how to represent model weights, activations, and attention key-value caches with fewer bits while preserving useful behavior and making deployment more efficient. Post-training methods such as GPTQ and AWQ use calibration data to round weights, while quantization-aware training, mixed-precision allocation, rotations, and outlier handling aim to reduce errors that accumulate across layers. Work also co-designs number formats and GPU, CPU, and edge-device kernels, evaluating trade-offs with language-model perplexity, zero-shot and reasoning benchmarks, memory, latency, and energy. Four-bit inference is often practical, but performance at very low bit widths remains model- and task-dependent, and an open challenge is ensuring that gains in aggregate accuracy do not hide losses in reasoning, safety, fairness, or uncertainty.

Latest papers

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388 papers84 papers in the last four weeks, up 121% on the four weeks before. 0.5% of all new papers.

Mar 9, 2026

SERQ: Saliency-Aware Low-Rank Error Reconstruction for LLM Quantization

Post-training quantization (PTQ) has emerged as a prevailing technique for deploying large language models (LLMs) efficiently in terms of both memory and computation, across edge devices and server platforms. Existing PTQ methods primarily aim to reduce precision in weights and activations by mitigating quantization errors caused by channel-wise outlier activations (e.g., pre-quantization scaling, online transformations, or low-rank error reconstruction). Among these approaches, error reconstruction with low-rank adaptation (LoRA) has proven particularly effective, as it introduces a lightweight auxiliary computation path without requiring heavy optimization or additional online layers. However, prior studies reveal severe accuracy degradation under W4A4 settings, and conventional low-rank adaptations rely on two sequential factors, necessitating intermediate quantization during inference and thereby limiting low-precision efficiency. In this work, we propose SERQ, a saliency-aware error reconstruction method for low-bit LLM inference that employs a single low-rank compensation matrix. SERQ preserves efficient 4-bit matrix multiplication in linear layers by jointly mitigating quantization errors arising from both activation and weight saliency through three stages: (1) static activation flattening, (2) saliency-aware error reconstruction, and (3) offline weight permutation. The method incurs additional computation only for low-rank error reconstruction via a single decomposition, while all other operations are performed offline, thereby keeping latency overhead minimal. Empirically, SERQ outperforms prior error reconstruction methods under both W4A8 and W4A4 settings, and achieves higher accuracy than state-of-the-art rotation-based W4A4 approaches, while substantially reducing calibration complexity. Code is available at https://github.com/acalabys/SERQ

Yeonsik Park, Hyeonseong Kim, Seungkyu Choi

Kyung Hee University · Yonsei University

LLM QuantizationPost-Training QuantizationLow-Bit QuantizationQuantization-Aware LoRAActivation Quantization
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Mar 5, 2026

Diagnosing FP4 inference: a layer-wise and block-wise sensitivity analysis of NVFP4 and MXFP4

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

Musa Cim, Burak Topcu, Mahmut Taylan Kandemir

Department of Computer Science and Engineering The Pennsylvania State University University Park, PA, USA

Quantization Sensitivity AnalysisLLM QuantizationNeural Network Quantization4-Bit QuantizationAttention Quantization
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Mar 5, 2026

Sparse-BitNet: 1.58-bit LLMs are Naturally Friendly to Semi-Structured Sparsity

Semi-structured N:M sparsity and low-bit quantization (e.g., 1.58-bit BitNet) are two promising approaches for improving the efficiency of large language models (LLMs), yet they have largely been studied in isolation. In this work, we investigate their interaction and show that 1.58-bit BitNet is naturally more compatible with N:M sparsity than full-precision models. To study this effect, we propose Sparse-BitNet, a unified framework that jointly applies 1.58-bit quantization and dynamic N:M sparsification while ensuring stable training for the first time. Across multiple model scales and training regimes (sparse pretraining and dense-to-sparse schedules), 1.58-bit BitNet consistently exhibits smaller performance degradation than full-precision baselines at the same sparsity levels and can tolerate higher structured sparsity before accuracy collapse. Moreover, using our custom sparse tensor core, Sparse-BitNet achieves substantial speedups in both training and inference, reaching up to 1.30X. These results highlight that combining extremely low-bit quantization with semi-structured N:M sparsity is a promising direction for efficient LLMs. Code available at https://github.com/AAzdi/Sparse-BitNet

Di Zhang, Xun Wu, Shaohan Huang +9

Microsoft Research · Peking University · South China University of Technology

LLM Inference EfficiencyLLM QuantizationLow-Bit QuantizationStructured Sparsity
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Mar 5, 2026

WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantization

This paper considers the problem of converting a given dense linear layer to low precision. The tradeoff between compressed length and output discrepancy is analyzed information theoretically (IT). It is shown that a popular GPTQ algorithm may have an arbitrarily large gap to the IT limit. To alleviate this problem, a novel algorithm, termed ``WaterSIC'', is proposed and is shown to be within a rate gap of 0.255 bits to the IT limit, uniformly over all possible covariance matrices of input activations. The key innovation of WaterSIC's is to allocate different quantization rates to different columns (in-features) of the weight matrix, mimicking the classical IT solution known as "waterfilling". Applying WaterSIC to the Llama and Qwen family of LLMs establishes new state-of-the-art performance for all quantization rates from 1 to 4 bits. Our code is available at https://github.com/egorlifar/watersic.

Egor Lifar, Semyon Savkin, Or Ordentlich +1

MIT · Independent Researcher · Hebrew University of Jerusalem

Neural Network QuantizationLLM QuantizationPost-Training QuantizationWeight-Only QuantizationInformation-Theoretic Lower Bounds
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Mar 4, 2026

Dissecting Quantization Error: A Concentration-Alignment Perspective

Quantization can drastically increase the efficiency of large language and vision models, but typically incurs an accuracy drop. Recently, function-preserving transforms (e.g. rotations, Hadamard transform, channel-wise scaling) have been successfully applied to reduce post-training quantization error, yet a principled explanation remains elusive. We analyze linear-layer quantization via the signal-to-quantization-noise ratio (SQNR), showing that for uniform integer quantization at a fixed bit width, SQNR decomposes into (i) the concentration of weights and activations (capturing spread and outliers), and (ii) the alignment of their dominant variation directions. This reveals an actionable insight: beyond concentration - the focus of most prior transforms (e.g. rotations or Hadamard) - improving alignment between weight and activation can further reduce quantization error. Motivated by this, we introduce block Concentration-Alignment Transforms (CAT), a lightweight linear transformation that uses a covariance estimate from a small calibration set to jointly improve concentration and alignment, approximately maximizing SQNR. Experiments across several LLMs show that CAT consistently matches or outperforms prior transform-based quantization methods at 4-bit precision, confirming the insights gained in our framework.

Marco Federici, Boris van Breugel, Paul Whatmough +1

Qualcomm AI Research

LLM Quantization4-Bit QuantizationPost-Training QuantizationNeural Network QuantizationQuantization
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Mar 4, 2026

Bielik-Q2-Sharp: A Comparative Study of Extreme 2-bit Quantization Methods for a Polish 11B Language Model

We present Bielik-Q2-Sharp, the first systematic academic evaluation of extreme 2-bit quantization applied to a Polish large language model. Using Bielik-11B-v2.3-Instruct (11B parameters, Mistral architecture) as our base model, we compare six state-of-the-art post-training quantization methods -- QuIP#, SpinQuant+GPTQ, ButterflyQuant, QTIP, VPTQ, and AQLM -- all calibrated on a Polish-language corpus (CulturaX-PL) with shared Hessian matrices. Our best variant (QuIP# E8P12) achieves 71.92% across 22 Polish benchmarks versus 72.07% for the IQ2_XXS baseline -- within statistical noise, at a modest size premium (3.26 GB vs. ~2.6 GB). On eq_bench, our method scores 47.14 versus 43.53 (+3.6pp), suggesting superior preservation of higher-order reasoning. QTIP achieves the best per-bit efficiency (79.4% MC acc_norm at ~2.4 bpw, 3.27 GB), matching VPTQ's quality at 35% smaller size. We additionally document a MC-generation dissociation phenomenon where rotation-based methods preserve log-likelihood quality but fail catastrophically at autoregressive generation. The entire project was conducted by a single independent researcher on cloud GPUs (vast.ai) within a $285 budget. All models, Hessians, and evaluation logs are publicly available.

Jakub Prejzner

BitSharp, Independent Researcher, Rzeszów, Poland

QuantizationLLM QuantizationPost-Training QuantizationLow-Bit QuantizationLanguage ModelingLLM Evaluation
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Mar 2, 2026

FreeAct: Freeing Activations for LLM Quantization

Quantization is pivotal for mitigating the significant memory and computational overhead of Large Language Models (LLMs). While emerging transformation-based methods have successfully enhanced quantization by projecting feature spaces onto smoother manifolds using orthogonal matrices, they typically enforce a rigid one-to-one transformation constraint. This static approach fails to account for the dynamic patterns inherent in input activations, particularly within diffusion LLMs (dLLMs) and Multimodal LLMs (MLLMs), where varying token types exhibit distinct distributions. To advance this, we propose FreeAct, a novel quantization framework that relaxes the static one-to-one constraint to accommodate dynamic activation disparities. Theoretically, we leverage the rank-deficient nature of activations to derive a solution space that extends beyond simple inverse matrices, enabling the decoupling of activation transformations from weights. Methodologically, FreeAct identifies token-specific dynamics (i.e., vision v.s. text, or masked tokens) and allocates distinct transformation matrices to the activation side, while maintaining a unified, static transformation for the weights. Extensive experiments across dLLMs and MLLMs demonstrate that FreeAct significantly outperforms baselines, up to 5.3% performance improvement, with in-depth analyses. Our code will be publicly released.

Xiaohao Liu, Xiaobo Xia, Manyi Zhang +6

National University of Singapore · Huawei Technology · Central South University

LLM QuantizationActivation QuantizationVLM QuantizationRotation-Based Quantization
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Feb 26, 2026

pQuant: Towards Effective Low-Bit Language Models via Decoupled Linear Quantization-Aware Training

Quantization-Aware Training from scratch has emerged as a promising approach for building efficient large language models (LLMs) with extremely low-bit weights (sub 2-bit), which can offer substantial advantages for edge deployment. However, existing methods still fail to achieve satisfactory accuracy and scalability. In this work, we identify a parameter democratization effect as a key bottleneck: the sensitivity of all parameters becomes homogenized, severely limiting expressivity. To address this, we propose pQuant, a method that decouples parameters by splitting linear layers into two specialized branches: a dominant 1-bit branch for efficient computation and a compact high-precision branch dedicated to preserving the most sensitive parameters. Through tailored feature scaling, we explicitly guide the model to allocate sensitive parameters to the high-precision branch. Furthermore, we extend this branch into multiple, sparsely-activated experts, enabling efficient capacity scaling. Extensive experiments indicate our pQuant achieves state-of-the-art performance in extremely low-bit quantization.

Wenzheng Zhang, Bingzheng Liu, Yang Hu +3

School of Computer Science, Peking University · College of Future Information Technology, Fudan University · Center for Information Research, Academy of Military Sciences +2

LLM QuantizationLow-Bit QuantizationNeural Network QuantizationQuantization-Aware TrainingMixture-of-Experts Quantization
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Feb 21, 2026

MoBiQuant: Mixture-of-Bits Quantization for Token-Adaptive Any-Precision LLM

Dynamic runtime latency and memory constraints necessitate flexible large language model (LLM) deployment, where an LLM can be inferred with various quantization precisions based on available computational resources. Recent work on such any-precision quantization either relies on hardware-inefficient vector quantization or induces additional scaling factors when switching between bit-widths. Meanwhile, existing post-training quantization (PTQ) methods calibrated for a fixed low precision show poor generalizability under runtime precision change. In this work, we attribute the source of poor generalization across bit-widths to a precision-dependent outlier migration phenomenon where the distribution of PTQ-sensitive tokens changes across precisions. Motivated by this observation, we propose MoBiQuant, a novel any-precision Mixture-of-Bits quantization framework that adjusts weight precision for flexible LLM inference based on token sensitivity. Specifically, we propose a many-in-one recursive residual quantization that can iteratively reconstruct higher-precision weights at runtime and mitigates outlier migration with a token-aware router to dynamically select the optimal inference precision of each token.Extensive experiments show that MoBiQuant matches or surpasses frontier single-precision PTQ while exhibiting strong elasticity, achieving significant memory savings and throughput gains of up to 1.34×1.34\times over state-of-the-art any-precision methods.

Dongwei Wang, Jinhee Kim, Seokho Han +8

University of Arizona · Panasonic AI Lab · Duke University +2

LLM QuantizationNeural Network QuantizationMixed-Precision QuantizationPost-Training Quantization
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Feb 20, 2026

SPQ: An Ensemble Technique for Large Language Model Compression

This study presents an ensemble technique, SPQ (SVD-Pruning-Quantization), for large language model (LLM) compression that combines variance-retained singular value decomposition (SVD), activation-based pruning, and post-training linear quantization. Each component targets a different source of inefficiency: i) pruning removes redundant neurons in MLP layers, ii) SVD reduces attention projections into compact low-rank factors, iii) and 8-bit quantization uniformly compresses all linear layers. At matched compression ratios, SPQ outperforms individual methods (SVD-only, pruning-only, or quantization-only) in perplexity, demonstrating the benefit of combining complementary techniques. Applied to LLaMA-2-7B, SPQ achieves up to 75% memory reduction while maintaining or improving perplexity (e.g., WikiText-2 5.47 to 4.91) and preserving accuracy on downstream benchmarks such as C4, TruthfulQA, and GSM8K. Compared to strong baselines like GPTQ and SparseGPT, SPQ offers competitive perplexity and accuracy while using less memory (6.86 GB vs. 7.16 GB for GPTQ). Moreover, SPQ improves inference throughput over GPTQ, achieving up to a 1.9x speedup, which further enhances its practicality for real-world deployment. The effectiveness of SPQ's robust compression through layer-aware and complementary compression techniques may provide practical deployment of LLMs in memory-constrained environments. Code is available at: https://github.com/JiaminYao/SPQ_LLM_Compression/

Jiamin Yao, Eren Gultepe

Dept. of Computer Science, Southern Illinois University Edwardsville, Edwardsville, USA

LLM CompressionLLM QuantizationLLM PruningLLM Inference AccelerationPost-Training Quantization
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Feb 17, 2026

1-Bit Wonder: Improving QAT Performance in the Low-Bit Regime through K-Means Quantization

Quantization-aware training (QAT) is an effective method to drastically reduce the memory footprint of LLMs while keeping performance degradation at an acceptable level. However, the optimal choice of quantization format and bit-width presents a challenge in practice. The full design space of quantization is not fully explored in the context of QAT, and the precise trade-off between quantization and downstream performance is poorly understood, as comparisons often rely solely on perplexity-based evaluations. In this work, we address these shortcomings with an empirical study of QAT in the low-bit regime. We show that k-means based weight quantization outperforms integer formats and can be implemented efficiently on standard hardware. Furthermore, we find that, under a fixed inference memory budget, the best performance on generative downstream tasks is achieved with 11-bit quantized weights.

Sohir Maskey, Constantin Eichenberg, Johannes Messner +1

Aleph Alpha Research · Graphcore Research

QuantizationLLM QuantizationLow-Bit QuantizationQuantization-Aware TrainingWeight-Only QuantizationVector Quantization
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Feb 11, 2026

QTALE: Quantization-Robust Token-Adaptive Layer Execution for LLMs

Large language models (LLMs) demand substantial computational and memory resources, posing challenges for efficient deployment. Two complementary approaches have emerged to address these issues: token-adaptive layer execution, which reduces floating-point operations (FLOPs) by selectively bypassing layers, and quantization, which lowers memory footprint by reducing weight precision. However, naively integrating these techniques leads to additional accuracy degradation due to reduced redundancy in token-adaptive models. We propose QTALE (Quantization-Robust Token-Adaptive Layer Execution for LLMs), a novel framework that enables seamless integration of token-adaptive execution with quantization while preserving accuracy. Conventional token-adaptive methods reduce redundancy in two ways: (1) by limiting the diversity of training paths explored during fine-tuning, and (2) by lowering the number of parameters actively involved in inference. To overcome these limitations, QTALE introduces two key components: (1) a training strategy that ensures diverse execution paths are actively explored during fine-tuning, and (2) a post-training mechanism that allows flexible adjustment of the execution ratio at inference to reintroduce redundancy when needed. Experimental results show that QTALE enables seamless integration of token-adaptive layer execution with quantization, while keeping the accuracy gap to quantization-only models below 0.5% on CommonsenseQA benchmarks. By combining tokenadaptive execution for FLOPs reduction and quantization for memory savings, QTALE provides an effective solution for efficient LLM deployment.

Kanghyun Noh, Jinheon Choi, Yulhwa Kim

Department of Semiconductor Convergence Engineering, Sungkyunkwan University · Department of Electrical and Computer Engineering, Sungkyunkwan University · Department of Semiconductor Systems Engineering, Sungkyunkwan University

LLM QuantizationLLM CompressionLLM Inference Acceleration
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Feb 5, 2026

Investigating Social Bias Changes in Quantized Language Models

Post-training quantization reduces the memory needed to run large language models but alters their social biases in ways that aggregate metrics fail to capture. We present the first large-scale study of 50 quantized models evaluated on PostTrainingBiasBench, a unified benchmark of 13 closed- and open-ended bias datasets. We identify a phenomenon we term quantization-induced bias flipping, in which quantization causes models to change responses from biased to unbiased and vice versa, up to 21% of the time, despite no change in aggregate bias scores. These flips are strongly associated with model uncertainty, where the responses with high uncertainty are 3-11x more likely to change than the confident ones. Quantization strength amplifies this effect, with 4-bit quantized models exhibiting 4-6x more behavioral changes than 8-bit quantized models. Critically, these changes create asymmetric impacts across demographic groups, where bias can worsen by up to 18.6% for some groups while improving by 14.1% for others, yielding misleadingly neutral aggregate outcomes. Larger models show no consistent robustness advantage, and group-specific shifts vary unpredictably across model families. Our findings demonstrate that compression fundamentally alters bias patterns, requiring crucial post-quantization evaluation and interventions to ensure reliability in practice.

Stanley Z. Hua, Sanae Lotfi, Irene Y. Chen

UC Berkeley & UCSF · Meta Superintelligence Labs

LLM QuantizationSocial Bias in Language ModelsLanguage Model Bias EvaluationLinguistic Bias in Language ModelsPost-Training QuantizationNeural Network Quantization
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Feb 3, 2026

MatGPTQ: Efficient and Accurate Inference over Nested Quantized Models

Matryoshka Quantization (MatQuant), Any-Precision-LLM (AP) and AnyBCQ (AB) are recent quantization approaches showing that a single integer-quantized model can be served across multiple precisions. In this paradigm, lower-precision models are extracted from a higher-precision model by simply reading fewer bits of the weights. This enables a single checkpoint to cover a wide range of memory and latency budgets, but makes both quantization and efficient execution substantially harder. Existing methods rely on expensive quantization-aware training (QAT) or gradient-based post-training quantization (PTQ) rather than fast one-shot PTQ, and offer limited system support: dedicated kernels are either missing or restricted to single- or small-batch decoding. We address these limitations with Post-Training Matryoshka Quantization (MatGPTQ), an end-to-end pipeline for nested-model quantization and inference. MatGPTQ casts Matryoshka quantization as multi-precision error compensation, producing a single "sliceable" parent model jointly optimized for multiple target precisions in one pass over a small calibration set. We further refine the MatQuant representation so that an rr-bit model reads exactly rr bits, and introduce the first dedicated inference kernels for this format, supporting batch sizes beyond one and integrated into vLLM. Across standard LLMs and benchmarks, MatGPTQ outperforms MatQuant while remaining competitive with AP and AB at the smallest checkpoint size, and our kernels achieve end-to-end speedups of up to 3.5×\times over BF16 at the low-bit regime. Overall, MatGPTQ makes nested quantized models practical to serve from a single, compact checkpoint. Code is available at https://github.com/IST-DASLab/MatGPTQ.

Maximilian Kleinegger, Elvir Crnčević, Dan Alistarh

1Vienna University of Technology, Vienna, Austria · Institute of Science & Technology Austria (ISTA), Vienna, Austria · 3Red Hat AI, Boston, USA

LLM QuantizationLLM Inference AccelerationPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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Jan 29, 2026

Benford's Law as a Distributional Prior for Post-Training Quantization of Large Language Models

Post-training quantization (PTQ) is a practical way to reduce the memory footprint of large language models, but low-bit quantization is sensitive to mismatches between the quantization codebook and the empirical weight/activation distributions. We revisit Benford-like leading-digit statistics as a lightweight diagnostic of scale-broad behavior in transformer tensors. Across several model families, we observe a consistent functional dichotomy: transformational nn.Linear weights tend to be Benford-like, whereas LayerNorm parameters systematically deviate. Motivated by this observation, we propose BenQ, a data-free PTQ codebook that uses a simple log-spaced grid as a proxy for scale-broad distributions and applies it selectively to transformational layers while keeping stability-critical parameters in higher precision. In 4-bit group-wise PTQ, BenQ consistently improves over uniform RTN and trades wins with NF4 across architectures and tasks, while remaining substantially simpler than optimization-based methods. We additionally report dynamic activation quantization as an exploratory stress test: the results show that log-spaced grids can reduce RTN failures in some families, but also reveal that outlier handling remains essential for reliable low-bit activation PTQ. Code is available at https://github.com/ufopcsilab/benford-quant.

Arthur Negrão, Pedro Silva, Vander L. S. Freitas +2

Postgraduate Program in Computer Science Federal University of Ouro Preto · Computing Department Federal University of Ouro Preto

LLM Quantization4-Bit QuantizationPost-Training QuantizationNeural Network Quantization
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Jan 17, 2026

Preserving Fairness and Safety in Quantized LLMs Through Critical Weight Protection

Quantization is widely adopted to reduce the computational cost of large language models (LLMs); however, its implications for fairness and safety, particularly in dynamic quantization and multilingual contexts, remain underexplored. In this work, we conduct a systematic study of how static and dynamic quantization methods impact fairness and safety across benchmarks measuring intrinsic and extrinsic bias and safety alignment. For fairness, we evaluate English, French, Dutch, Spanish, and Turkish; for safety, we focus on English, Korean, and Arabic. Our findings reveal that quantization consistently degrades fairness and safety, with dynamic methods demonstrating greater stability than static ones. Moreover, fairness degradation varies across languages, while safety deterioration is especially pronounced in non-English settings. To address these risks, we introduce Critical Weight Protection, a novel technique that identifies and preserves fairness- and safety-critical weights during quantization. This approach effectively mitigates bias and safety deterioration without costly retraining or alignment, maintaining trustworthiness while retaining efficiency.

Muhammad Alif Al Hakim, Alfan Farizki Wicaksono, Fajri Koto

Faculty of Computer Science, Universitas Indonesia · Mohamed bin Zayed University of Artificial Intelligence

LLM QuantizationMultilingual Language Model EvaluationLanguage Model Safety EvaluationLanguage Model Bias EvaluationNeural Network Quantization
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Jan 15, 2026

Activation Sensitivity as a Unifying Principle for Post-Training Quantization

Post-training quantization (PTQ) methods for large language models compress pretrained weights to low bit-widths without retraining by optimizing layer-local proxy objectives. Activation-aware scaling methods such as AWQ protect input channels with large activation norms, whereas second-order error-compensation methods such as GPTQ redistribute rounding error using the inverse of the unweighted input covariance matrix. We show that both paradigms -- along with diagonal Fisher quantization, block reconstruction, and Hadamard rotation methods -- are special cases of minimizing a single loss-derived quadratic form governed by gradient-weighted activation sensitivity. From a Gauss-Newton expansion of the task loss at a linear layer Y=XW⊤Y = X W^\top, we prove that under isotropic output curvature the expected excess loss from weight perturbation ΔWΔW reduces to 12doutTr⁡(ΔWHDΔW⊤)\frac{1}{2 d_{\mathrm{out}}}\operatorname{Tr}(ΔW H_D ΔW^\top), where HD=1nX⊤DXH_D = \frac{1}{n} X^\top D X weights each calibration token's outer product by its squared output-gradient norm Dtt=∥∇ytL∥22D_{tt} = \|\nabla_{y_t}\mathcal{L}\|_2^2. Within this framework, AWQ corresponds to a diagonal approximation of HDH_D with uniform token weights (D=InD = I_n) optimized via channel scaling, while GPTQ corresponds to Cholesky error compensation on HDH_D under D=InD = I_n. We derive closed-form optimal scaling exponents for diagonal sensitivity protection, formulate sensitivity-weighted Cholesky quantization (SAQ-GPTQ) on HDH_D, and prove bounds on token-gradient heterogeneity bias, cross-layer error amplification across residual blocks, and finite-sample calibration concentration. Controlled numerical simulations confirm that under token-gradient heterogeneity, replacing X⊤XX^\top X with X⊤DXX^\top D X preserves >99%>99\% top-channel saliency recall and reduces INT3/INT4 excess loss by roughly 3×3\times over unweighted GPTQ.

Bruce Changlong Xu

LLM QuantizationPost-Training QuantizationNeural Network QuantizationQuantization Sensitivity AnalysisWeight-Only Quantization
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Jan 12, 2026

ARCQuant: Boosting NVFP4 Quantization with Augmented Residual Channels for LLMs

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.

Haoqian Meng, Yilun Luo, Yafei Zhao +3

School of Computer Science and Technology, Tianjin University

LLM Quantization4-Bit QuantizationLLM Inference AccelerationQuantization Error CompensationPost-Training QuantizationNeural Network Quantization
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Dec 22, 2025

When Less is More: 8-bit Quantization Improves Continual Learning in Large Language Models

Catastrophic forgetting poses a fundamental challenge in continual learning, particularly when models are quantized for deployment efficiency. We systematically investigate the interplay between quantization precision (FP16, INT8, INT4) and replay buffer strategies in large language models, revealing unexpected dynamics. While FP16 achieves superior initial task performance (74.44% on NLU), we observe a striking inversion on subsequent tasks: quantized models outperform FP16 by 8-15% on final task forward accuracy, with INT4 achieving nearly double FP16's performance on Code generation (40% vs 20%). Critically, even minimal replay buffers (0.1%) dramatically improve retention - increasing NLU retention after Math training from 45% to 65% across all precision levels - with INT8 consistently achieving the optimal balance between learning plasticity and knowledge retention. We hypothesize that quantization-induced noise acts as implicit regularization, preventing the overfitting to new task gradients that plagues high-precision models. These findings challenge the conventional wisdom that higher precision is always preferable, suggesting instead that INT8 quantization offers both computational efficiency and superior continual learning dynamics. Our results provide practical guidelines for deploying compressed models in continual learning scenarios: small replay buffers (1-2%) suffice for NLU tasks, while Math and Code benefit from moderate buffers (5-10%), with quantized models requiring less replay than FP16 to achieve comparable retention. Code is available at https://github.com/Festyve/LessIsMore.

Michael S. Zhang, Rishi A. Ruia, Arnav Kewalram +3

Algoverse

LLM QuantizationContinual Learning for LLMsReplay-Based Continual LearningCatastrophic Forgetting
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Nov 9, 2025

You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations

Many LLM applications require only narrow capabilities, yet standard post-training quantization (PTQ) methods allocate precision without considering the target task. This can waste bits on layers that are less relevant to the task signal while over-compressing layers that are critical for downstream behavior. We propose Task-Aware Quantization (TAQ), a training-free, weight-only mixed-precision PTQ framework that uses a small set of unlabeled task calibration prompts to allocate higher precision to task-relevant transformer layers under a fixed bit budget. TAQ estimates layer importance from hidden representations and output sensitivity, and we instantiate it with three scoring rules: TAQ-IS, based on activation information and stability; TAQ-KL, based on output-distribution sensitivity under a quantization-noise proxy; and TAQ-O, a label-informed oracle diagnostic for analyzing layer sensitivity. Across several benchmarks, TAQ outperforms task-agnostic baselines such in most settings, with especially strong gains in the accuracy--memory ratio. We further validate that these gains translate to real deployment behavior through hardware throughput and latency measurements, and analyze calibration robustness and residual-stream error propagation. Overall, TAQ turns mixed-precision PTQ from a model-centric compression step into a task-conditioned precision-allocation problem. A reference implementation is available at \includegraphics[height=1em]{imgs/github-mark.png}.

Amit LeVi, Raz Lapid, Rom Himelstein +3

1Technion—Israel Institute of Technology · 2Intuit · 3Ben-Gurion University of the Negev +1

Weight-Only QuantizationMixed-Precision QuantizationLLM QuantizationPost-Training QuantizationNeural Network QuantizationQuantization+1
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Sep 28, 2025

LUQ: Layerwise Ultra-Low Bit Quantization for Multimodal Large Language Models

Large Language Models (LLMs) with multimodal capabilities have revolutionized vision-language tasks, but their deployment often requires huge memory and computational resources. Post-training quantization (PTQ) has successfully compressed language models to as low as 1-bit precision, its effectiveness for multimodal LLMs (MLLMs) remains unexplored. In this paper, we present the first method for ultra-low-bit (<4-bit) quantization of MLLMs. Our analysis reveals that multimodal tokens and intermediate layer activations produced by them exhibit significantly higher entropy compared to text tokens, indicating greater functional complexity that makes MLLMs less tolerant to ultra-low bit quantization. However, this entropy varies significantly across layers, with some layers producing lower-entropy activation distributions that we empirically show can better tolerate ultra-low bit quantization. Existing PTQ methods optimize weight quantization within each layer but apply the same target precision uniformly, ignoring this variation in complexity across layers. Building on this insight, we propose LUQ: Layerwise Ultra-Low Bit Quantization, which characterizes each transformer layer's functional complexity via its output activation entropy and selectively applies ultra-low bit quantization to layers encoding simpler, more compressible functions. We also show that multimodal calibration (image and text tokens) boosts VQA performance in the ultra-low bit regime. Evaluated on LLaVA-1.5 and Qwen-2.5-VL across 9 VQA benchmarks, LUQ models use 40% and 31% less memory than their 4-bit counterparts while exhibiting less than 10% degradation on MME.

Shubhang Bhatnagar, Andy Xu, Kar-Han Tan +1

University of Illinois Urbana-Champaign · Work done as an intern at HP Inc. · University of California, Los Angeles +1

Mixed-Precision QuantizationLLM QuantizationVLM QuantizationMultimodal Large Language ModelsMultimodal Foundation ModelsPost-Training Quantization+1
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Sep 22, 2025

On-the-Fly Adaptation to Quantization: Configuration-Aware LoRA for Efficient Fine-Tuning of Quantized LLMs

As increasingly large pre-trained models are released, deploying them on edge devices for privacy-preserving applications requires effective compression. Recent works combine quantization with the fine-tuning of high-precision LoRA adapters, which can substantially reduce model size while mitigating the accuracy loss from quantization. However, edge devices have inherently heterogeneous capabilities, while performing configuration-wise fine-tuning for every quantization setting is computationally prohibitive. In this paper, we propose CoA-LoRA, a method that dynamically adjusts the LoRA adapter to arbitrary quantization configurations (i.e., the per-layer bit-width choices of a pre-trained model) without requiring repeated fine-tuning. This is accomplished via a configuration-aware model that maps each configuration to its low-rank adjustments. The effectiveness of this model critically depends on the training configuration set, a collection of configurations chosen to cover different total bit-width budgets. However, constructing a high-quality configuration set is non-trivial. We therefore design a Pareto-based configuration search that iteratively optimizes the training configuration set, yielding more precise low-rank adjustments. Our experiments demonstrate that, unlike the state-of-the-art methods that require fine-tuning a separate LoRA adapter for each configuration, CoA-LoRA incurs no additional time cost while achieving comparable or even superior performance to those methods.

Rongguang Ye, Ming Tang, Edith C. H. Ngai

Southern University of Science and Technology · The University of Hong Kong

Mixed-Precision QuantizationLLM QuantizationLow-Rank AdaptationQuantization-Aware LoRAParameter-Efficient Fine-Tuning
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Sep 18, 2025

Fair-GPTQ: Bias-Aware Quantization for Large Language Models

The high memory demands of generative language models have drawn attention to quantization, which reduces memory usage by mapping model weights to lower-precision integers. However, recent empirical studies show that, while efficient, quantization can increase the likelihood of generating biased outputs and degrade performance on fairness benchmarks. In this work, we draw new links between quantization and model fairness by adding explicit group-fairness constraints to the quantization objective and introduce Fair-GPTQ, the first quantization method explicitly designed to reduce unfairness in large language models. The added constraints guide the learning of the rounding operation toward less-biased text generation for protected groups. Specifically, we focus on stereotype generation involving occupational bias and discriminatory language spanning gender, race, and religion. Fair-GPTQ has minimal impact on performance, preserving at least 90% of baseline accuracy on zero-shot benchmarks, reduces unfairness relative to a half-precision model, and retains the memory and speed benefits of 4-bit quantization.

Irina Proskurina, Guillaume Metzler, Julien Velcin

Université Claude Bernard Lyon 1, Université Lumière Lyon 2, ERIC · École Centrale de Lyon, LIRIS, CNRS UMR 5205

LLM QuantizationSocial Bias in Language ModelsAlgorithmic Fairness
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Jul 24, 2025

Squeeze10-LLM: Squeezing LLMs' Weights by 10 Times via a Staged Mixed-Precision Quantization Method

Deploying large language models (LLMs) is challenging due to their massive parameters and high computational costs. Ultra low-bit quantization can significantly reduce storage and accelerate inference, but extreme compression (i.e., mean bit-width <= 2) often leads to severe performance degradation. To address this, we propose Squeeze10-LLM, effectively "squeezing" 16-bit LLMs' weights by 10 times. Specifically, Squeeze10-LLM is a staged mixed-precision post-training quantization (PTQ) framework and achieves an average of 1.6 bits per weight by quantizing 80% of the weights to 1 bit and 20% to 4 bits. We introduce Squeeze10LLM with two key innovations: Post-Binarization Activation Robustness (PBAR) and Full Information Activation Supervision (FIAS). PBAR is a refined weight significance metric that accounts for the impact of quantization on activations, improving accuracy in low-bit settings. FIAS is a strategy that preserves full activation information during quantization to mitigate cumulative error propagation across layers. Experiments on LLaMA and LLaMA2 show that Squeeze10-LLM achieves state-of-the-art performance for sub-2bit weight-only quantization, improving average accuracy from 43% to 56% on six zero-shot classification tasks--a significant boost over existing PTQ methods.

Qingcheng Zhu, Yangyang Ren, Linlin Yang +6

Beihang University · Communication University of China · Beijing Jiaotong University

Mixed-Precision QuantizationLLM QuantizationWeight-Only QuantizationPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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Jul 23, 2025

A Comprehensive Evaluation on Quantization Techniques for Large Language Models

For large language models (LLMs), post-training quantization (PTQ) significantly reduces memory and computational overhead. Despite rapid advancements, existing papers often lack experiments on the same ground. In addition, since quantization solutions typically contain multiple components, it is important to analyze the connections among numerous existing methods to gain an in-depth understanding of this field. To bridge these gaps, we conduct an up-to-date and extensive review of the state-of-the-art methods and perform comprehensive evaluations of low-bit quantization on representative text-only LLMs on the same ground to ensure fair comparisons. To our knowledge, this fair and extensive investigation remains critically important yet significantly underexplored in the research community. To better understand the connections, we first decouple published quantization into two steps: pre-quantization transformation to reduce outliers, and quantization error mitigation to offset performance loss. Second, we extensively evaluate the impact of quantization settings, including granularity and symmetry. Third, we analyze the performance of the latest MXFP4 and NVFP4 data formats. Our experimental results first demonstrate that optimizing rotation and scaling yields the best pre-quantization transformation, while combining low-rank compensation with GPTQ occasionally outperforms using GPTQ alone. Second, we verify that finer granularity improves performance at the cost of storage and asymmetric quantization benefits activations significantly more than weights. Third, we find that the format and precision of scaling factors have a significant impact on performance; notably, rotation-based transformation is effective for INT4 but demonstrates little improvement for MXFP4 and NVFP4, inspiring further investigation in this field.

Yutong Liu, Cairong Zhao, Guosheng Hu

School of Computer Science and Technology, Tongji University, Shanghai 201804, China · School of Engineering Math and Technology, University of Bristol, BS8 1QU, UK

LLM QuantizationPost-Training QuantizationLow-Bit Quantization4-Bit Quantization
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Jun 5, 2025

FPTQuant: Function-Preserving Transforms for LLM Quantization

Large language models (LLMs) require substantial compute, and thus energy, at inference time. While quantizing weights and activations is effective at improving efficiency, naive quantization of LLMs can significantly degrade performance due to large magnitude outliers. This paper describes FPTQuant, which introduces three novel, lightweight, and expressive function-preserving transforms (FPTs) to facilitate quantization of transformers: (1) a mergeable pre-RoPE transform for queries and keys, (2) a mergeable transform for values, and (3) a cheap, dynamic per-token scaling transform. By leveraging the equivariances and independencies inherent to canonical transformer operation, we designed these FPTs to maintain the model's function while shaping the intermediate activation distributions to be more quantization friendly. FPTQuant requires no custom kernels and adds virtually no overhead during inference. The FPTs are trained both locally to reduce outliers, and end-to-end such that the outputs of the quantized and full-precision models match. FPTQuant enables static INT4 quantization with minimal overhead and shows SOTA speed-up of up to 3.9X over FP. Empirically, FPTQuant has an excellent accuracy-speed trade-off -- it is performing on par or exceeding most prior work and only shows slightly lower accuracy compared to a method that is up to 29% slower.

Boris van Breugel, Yelysei Bondarenko, Paul Whatmough +1

Qualcomm AI Research, Amsterdam, Netherlands

LLM QuantizationLLM Inference AccelerationActivation QuantizationLow-Bit Quantization
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Jan 13, 2025

FlexQuant: Elastic Quantization Framework for Locally Hosted LLM on Edge Devices

Deploying LLMs on edge devices presents serious technical challenges. Memory elasticity is crucial for edge devices with unified memory, where memory is shared and fluctuates dynamically. Existing solutions suffer from either poor transition granularity or high storage costs. We propose FlexQuant, a novel elasticity framework that generates an ensemble of quantized models, providing an elastic hosting solution with 31x more deployment options, 15x granularity improvement, and 10x storage reduction compared to SoTA methods. FlexQuant works with most quantization methods and creates a family of trade-off options under various storage limits through our pruning method. It brings great performance and flexibility to the edge deployment of LLMs.

Yuji Chai, Mujin Kwun, David Brooks +1

Harvard John A. Paulson School Of Engineering And Applied Sciences Cambridge, Massachusetts, USA

LLM QuantizationOn-Device Language Model InferenceMemory-Efficient Inference
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Jun 11, 2024

TernaryLLM: Ternarized Large Language Model

Large language models (LLMs) have achieved remarkable performance on Natural Language Processing (NLP) tasks, but they are hindered by high computational costs and memory requirements. Ternarization, an extreme form of quantization, offers a solution by reducing memory usage and enabling energy-efficient floating-point additions. However, applying ternarization to LLMs faces challenges stemming from outliers in both weights and activations. In this work, observing asymmetric outliers and non-zero means in weights, we introduce Dual Learnable Ternarization (DLT), which enables both scales and shifts to be learnable. We also propose Outlier-Friendly Feature Knowledge Distillation (OFF) to recover the information lost in extremely low-bit quantization. The proposed OFF can incorporate semantic information and is insensitive to outliers. At the core of OFF is maximizing the mutual information between features in ternarized and floating-point models using cosine similarity. Extensive experiments demonstrate that our TernaryLLM surpasses previous low-bit quantization methods on the standard text generation and zero-shot benchmarks for different LLM families. Specifically, for one of the most powerful open-source models, LLaMA-3, our approach (W1.58A16) outperforms the previous state-of-the-art method (W2A16) by 5.8 in terms of perplexity on C4 and by 8.2% in terms of average accuracy on zero-shot tasks.

Tianqi Chen, Zhe Li, Weixiang Xu +6

Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Advanced Micro Devices, Inc., Beijing, China +1

LLM QuantizationTernary QuantizationQuantization-Aware Training
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