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.

Apr 11, 2026

Spike-driven Large Language Model

Current Large Language Models (LLMs) are primarily based on large-scale dense matrix multiplications. Inspired by the brain's information processing mechanism, we explore the fundamental question: how to effectively integrate the brain's spiking-driven characteristics into LLM inference. Spiking Neural Networks (SNNs) possess spike-driven characteristics, and some works have attempted to combine SNNs with Transformers. However, achieving spike-driven LLMs with billions of parameters, relying solely on sparse additions, remains a challenge in the SNN field. To address the issues of limited representational capacity and sparsity in existing spike encoding schemes at the LLM level, we propose SDLLM, a spike-driven large language model that eliminates dense matrix multiplications through sparse addition operations. Specifically, we use the plug-and-play gamma-SQP two-step spike encoding method to ensure that the quantization process aligns with the model's semantic space, mitigating representation degradation caused by binary spikes. Furthermore, we introduce bidirectional encoding under symmetric quantization and membrane potential clipping mechanisms, leading to spike trains with no or low firing counts dominating, significantly reducing the model's spike firing rate, while halving the number of time steps. Experimental results show that SDLLM not only significantly reduces inference costs but also achieves state-of-the-art task performance under the spike-based paradigm. For example, compared to previous spike-based LLMs, SDLLM reduces energy consumption by 7x and improves accuracy by 4.2%. Our model provides inspiration for the architecture design of the next generation of event-driven neuromorphic chips.

Han Xu, Xuerui Qiu, Baiyu Chen +7

Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China · Brain-Inspired Models Group, Beijing Academy of Artificial Intelligence, Beijing 100862, China +7

Spiking Language ModelsSpiking Neural NetworksLLM Inference AccelerationSpiking TransformersLLM Quantization
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Apr 11, 2026

SEPTQ: A Simple and Effective Post-Training Quantization Paradigm for Large Language Models

Large language models (LLMs) have shown remarkable performance in various domains, but they are constrained by massive computational and storage costs. Quantization, an effective technique for compressing models to fit resource-limited devices while preserving generative quality, encompasses two primary methods: quantization aware training (QAT) and post-training quantization (PTQ). QAT involves additional retraining or fine-tuning, thus inevitably resulting in high training cost and making it unsuitable for LLMs. Consequently, PTQ has become the research hotspot in recent quantization methods. However, existing PTQ methods usually rely on various complex computation procedures and suffer from considerable performance degradation under low-bit quantization settings. To alleviate the above issues, we propose a simple and effective post-training quantization paradigm for LLMs, named SEPTQ. Specifically, SEPTQ first calculates the importance score for each element in the weight matrix and determines the quantization locations in a static global manner. Then it utilizes the mask matrix which represents the important locations to quantize and update the associated weights column-by-column until the appropriate quantized weight matrix is obtained. Compared with previous methods, SEPTQ simplifies the post-training quantization procedure into only two steps, and considers the effectiveness and efficiency simultaneously. Experimental results on various datasets across a suite of models ranging from millions to billions in different quantization bit-levels demonstrate that SEPTQ significantly outperforms other strong baselines, especially in low-bit quantization scenarios.

Han Liu, Haotian Gao, Xiaotong Zhang +5

Dalian University of Technology, Dalian, China · Peking University, Beijing, China · Shenzhen MSU-BIT University, Shenzhen, China +1

LLM QuantizationPost-Training QuantizationNeural Network QuantizationLow-Bit Quantization
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Apr 10, 2026

EdgeRazor: A Lightweight Framework for Large Language Models via Mixed-Precision Quantization-Aware Distillation

Quantization has emerged as a mainstream approach for deploying Large Language Models (LLMs) on resource-constrained devices, yet compressing precision below 4-bit typically causes severe performance degradation or prohibitive retraining costs. In this paper, we propose EdgeRazor, a lightweight framework for LLMs via Mixed-Precision Quantization-Aware Distillation. It contains three modules: Structural Quantization with Mixed Precision for fine-grained control of bit-widths, Layer-Adaptive Feature Distillation that dynamically selects the most informative features for alignment, and Entropy-Aware KL Divergence for forward-reverse balance on both human-annotated and distilled datasets. Evaluations conducted on MobileLLM and Qwen families show that under weight-activation quantization, the 1.88-bit Qwen3-0.6B-EdgeRazor outperforms the state-of-the-art 2-bit baselines by 11.27 and surpasses the strongest 3-bit baselines by 4.38, while the quantized MobileLLM-350M-EdgeRazor requires a training budget 4-10×\times lower than the leading quantization-aware training method. In terms of efficiency, EdgeRazor achieves higher compression ratios at all bit-widths, and the 1.58-bit Qwen3-0.6B-EdgeRazor reduces storage from 1.11 GB to 0.19 GB while accelerating decoding by 15.16×\times over the 16-bit baseline. These results empirically validate the effectiveness and efficiency of EdgeRazor. The codes can be accessed from GitHub and Huggingface.

Shu-Hao Zhang, Le-Tong Huang, Xiang-Sheng Deng +5

National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210063, China · School of Intelligent Science and Technology, Nanjing University, Suzhou 215163, China · Microsoft AI, Beijing 100080, China +1

Quantization-Aware DistillationLLM QuantizationLLM CompressionMixed-Precision QuantizationQuantization-Aware TrainingLLM Inference Acceleration+1
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Apr 10, 2026

Quantisation Reshapes the Metacognitive Geometry of Language Models

We report that model quantisation restructures domain-level metacognitive efficiency in LLMs rather than degrading it uniformly. Evaluating Llama-3-8B-Instruct on the same 3,000 questions at Q5_K_M and f16 precision, we find that M-ratio profiles across four knowledge domains are uncorrelated between formats (Spearman rho = 0.00). Arts & Literature moves from worst-monitored (M-ratio = 0.606 at Q5_K_M) to best-monitored (1.542 at f16). Geography moves from well-monitored (1.210) to under-monitored (0.798). However, Type-2 AUROC profiles are perfectly stable across formats (rho = 1.00), localising the restructuring to the M-ratio normalisation rather than the underlying discrimination signal. This finding emerged from a pre-registered attempt to improve metacognition through domain-conditional training. We prescribed confidence-amplification SFT for the diagnosed weak domain, with matched-budget agnostic and wrong-prescription controls. All four confirmatory hypotheses were null (10,000 bootstrap resamples, seed = 42). The training successfully reshaped confidence distributions, doubling the NLP gap in Science from 0.076 to 0.152, but did not improve meta-d' because the diagnostic profile did not transfer across formats. Any system relying on domain-level M-ratio profiles has an unexamined dependency on inference format. Systems using AUROC_2 are safer. We release all code, pre-registrations, and trial-level data.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Language Model Self-AssessmentMetacognition in Language ModelsConfidence Estimation in Language ModelsLLM EvaluationLLM Quantization
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Apr 9, 2026

HiFloat4 Format for Language Model Pre-training on Ascend NPUs

Training large foundation models at low numerical precision is one of the most promising directions for reducing the compute and memory cost of modern AI. Recent 4-bit floating-point formats such as MXFP4 and NVFP4 can be applied to linear GEMM operations in LLMs, but their limited dynamic range introduces numerical instability that prior work addresses by stacking stabilization mechanisms, typically executed at higher precision and partially eroding the efficiency gains that motivate FP4. In this work, we argue that numerical format design is itself a first-class lever for stable FP4 training, and present the first systematic study of FP4 LLM pretraining on energy-efficient Huawei Ascend NPUs. We compare the recently proposed HiFloat4 (HiF4) format against both MXFP4 and NVFP4, holding one recipe fixed across all three formats across dense (OpenPangu-1B, Llama3-8B) and Mixture-of-Experts (Qwen3-MoE-30B) architectures and executing all linear and expert GEMMs in FP4. At matched storage --- NVFP4 and HiF4 both spend 4.5 bits per value --- the three formats differ far more in what they require before they will train at all than in final accuracy. HiF4 reaches a relative loss of 1.55% with no stabilization, below fully stabilized MXFP4 (1.79%) and below NVFP4 carrying the per-tensor scaling it cannot train without (2.00%); NVFP4 diverges under every combination of stochastic rounding and Hadamard transform we tried. Our results suggest that stable, accurate FP4 training does not require an ever-growing stack of stabilization techniques; it requires the right numerical format.

Mehran Taghian, Yunke Peng, Xing Huang +22

Huawei

Low-Precision TrainingLLM QuantizationLLM TrainingLanguage Model Pretraining
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Apr 9, 2026

Initialisation Determines the Basin: Efficient Codebook Optimisation for Extreme LLM Quantization

Additive quantization enables extreme LLM compression with O(1) lookup-table dequantization, making it attractive for edge deployment. Yet at 2-bit precision, it often fails catastrophically, even with extensive search and finetuning. We show that the dominant bottleneck is codebook initialisation. Greedy sequential initialisation frequently places the model in poor optimisation regions that subsequent beam search and PV-tuning struggle to overcome. We analyse this behaviour through the representational ratio \r{ho} = N/KM, which characterises the relationship between weight groups and codebook capacity, and propose OA-EM, an output-aware EM initialisation method using Hessian-weighted Mahalanobis distance. Across compression rates, search budgets, and three architectures (Llama 3.2 3B, Llama 3.1 8B, Qwen 2.5 3B), OA-EM consistently produces better solutions after PV-tuning and dominates the quality-compute frontier. The severity of the bottleneck scales with \r{ho}: moderate at 3 bpp but extreme at 2 bpp, where poor initialisation can degrade perplexity by orders of magnitude. More broadly, our results highlight the importance of optimisation geometry in compressed model spaces, where initialisation can dominate subsequent search and fine-tuning.

Ian W. Kennedy, Nafise Sadat Moosavi

Department of Computer Science, University of Sheffield, Sheffield, UK

LLM QuantizationNeural Network QuantizationLow-Bit QuantizationPost-Training QuantizationNeural Network Initialization
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Apr 9, 2026

Rethinking Residual Errors in Compensation-based LLM Quantization

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

Shuaiting Li, Juncan Deng, Kedong Xu +5

Zhejiang University · vivo Mobile Communication Co., Ltd

Quantization Error CompensationLLM QuantizationNeural Network QuantizationPost-Training QuantizationWeight-Only QuantizationLanguage Model Calibration
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Apr 9, 2026

Bit-by-Bit: Progressive QAT Strategy with Outlier Channel Splitting for Stable Low-Bit LLMs

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 11×\times 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.

Binxing Xu, Hao Gu, Lujun Li +8

Zhejiang University · Hong Kong University of Science and Technology · City University of Hong Kong

LLM QuantizationQuantization-Aware TrainingLow-Bit QuantizationActivation QuantizationActivation Outliers
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Apr 6, 2026

MUXQ: Mixed-to-Uniform Precision MatriX Quantization via Low-Rank Outlier Decomposition

Large language models (LLMs) have achieved outstanding performance across a wide range of natural language processing tasks, but their enormous parameter counts impose ubstantial memory and computational overheads. This challenge is particularly critical in NPU-based on-device environments, where FP16/FP32 computation is inefficient and integer (INT) quantization is therefore essential. However, existing methods, including ZeroQuant, LLM.int8(), and SmoothQuant, do not fully address input-activation outliers and the associated hardware inefficiencies. To overcome these limitations, we propose MUXQ (Mixed-to-Uniform Quantization). MUXQ detects outlier channels in input activations and introduces a small auxiliary matrix that redistributes outlier magnitudes across channels, thereby alleviating the outlier problem. This enables even activation outliers to be quantized at low-precision INT levels while preserving a hardware-friendly computation structure. Experiments on GPT-2 models at three scales (0.1B, 0.3B, and 0.7B parameters) using the WikiText-2 dataset show that MUXQ consistently achieves lower perplexity than naive quantization. In particular, under per-tensor quantization, MUXQ quantizes both activations and weights to INT8 while maintaining accuracy close to that of FP16. With only modest computational overhead, MUXQ enables stable low-precision inference and can be readily combined with other quantization techniques. These results suggest that MUXQ provides a promising direction for efficient and accurate LLM inference on edge devices.

Seoungsub Lee, In Seo Kim, Seon Wook Kim

School of Electrical Engineering, Korea University, Seoul, Korea

LLM QuantizationNeural Network QuantizationActivation QuantizationOn-Device Language Model Inference
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Apr 5, 2026

RUQuant: Towards Refining Uniform Quantization for Large Language Models

The increasing size and complexity of large language models (LLMs) have raised significant challenges in deployment efficiency, particularly under resource constraints. Post-training quantization (PTQ) has emerged as a practical solution by compressing models without requiring retraining. While existing methods focus on uniform quantization schemes for both weights and activations, they often suffer from substantial accuracy degradation due to the non-uniform nature of activation distributions. In this work, we revisit the activation quantization problem from a theoretical perspective grounded in the Lloyd-Max optimality conditions. We identify the core issue as the non-uniform distribution of activations within the quantization interval, which causes the optimal quantization point under the Lloyd-Max criterion to shift away from the midpoint of the interval. To address this issue, we propose a two-stage orthogonal transformation method, RUQuant. In the first stage, activations are divided into blocks. Each block is mapped to uniformly sampled target vectors using composite orthogonal matrices, which are constructed from Householder reflections and Givens rotations. In the second stage, a global Householder reflection is fine-tuned to further minimize quantization error using Transformer output discrepancies. Empirical results show that our method achieves near-optimal quantization performance without requiring model fine-tuning: RUQuant achieves 99.8% of full-precision accuracy with W6A6 and 97% with W4A4 quantization for a 13B LLM, within approximately one minute. A fine-tuned variant yields even higher accuracy, demonstrating the effectiveness and scalability of our approach.

Han Liu, Haotian Gao, Changya Li +4

Dalian University of Technology Dalian, China · Peking University Beijing, China · Macao Polytechnic University Macao, China

LLM QuantizationActivation QuantizationPost-Training QuantizationRotation-Based Quantization
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Apr 4, 2026

Improving Quantized Model Performance in Qualitative Analysis with Multi-Pass Prompt Verification

Quantized Large Language Models (LLMs) are used more often in qualitative analysis because they run fast and need fewer computing resources. This study examines how different lower bits quantization levels (8-bit, 4-bit, 3-bit, and 2-bit) and quantization types affect the performance of LLaMA-3.1 (8B) on qualitative analysis. The study uses expert and non-expert responses from 82 interview transcripts. Low-bit models often produce higher levels of hallucinations and unstable results, especially when reading non-expert language with unclear terms. To improve performance, we propose a quantization-aware multi-pass prompt verification method. This method guides the model through controlled steps that reduce hallucinations. It removes unreliable content and passes the results to the next transcript after verification, improving accuracy. To validate performance, human coders analyzed transcripts using NVivo and BF16 LLaMA. BF16 LLaMA-3.1 produced high-precision output but had semantic drift and hallucination. These errors were corrected manually. The corrected BF16 output and NVivo human coding were combined to create a gold-standard ground truth (GSGT) for thematic extraction and frequency analysis. The results show that 8-bit models stay closest to the GSGT. The 4-bit models lose accuracy but become stable when the proposed method is applied. The 3-bit and 2-bit models drop in performance because of heavy compression, but they improve with the proposed prompt design and verification. The study also finds that models at the same bit level behave differently depending on quantization type. Overall, the method helps low-resource LLMs become more stable, accurate, and suitable for qualitative research at lower cost.

Aisvarya Adeseye, Jouni Isoaho, Adeyemi Adeseye

University of Turku, Turku, Finland · Brilloconnetz Partners avoin yhtiö, Turku, Finland

LLM QuantizationLow-Bit QuantizationLLM Hallucination MitigationLLM Answer Verification
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Apr 2, 2026

Fast NF4 Dequantization Kernels for Large Language Model Inference

Large language models (LLMs) have grown beyond the memory capacity of single GPU devices, necessitating quantization techniques for practical deployment. While NF4 (4-bit NormalFloat) quantization enables 4×\times memory reduction, inference on current NVIDIA GPUs (e.g., Ampere A100) requires expensive dequantization back to FP16 format, creating a critical performance bottleneck. This paper presents a lightweight shared memory optimization that addresses this gap through principled memory hierarchy exploitation while maintaining full ecosystem compatibility. We compare our technique against the open-source BitsAndBytes implementation, achieving 2.0--2.2×\times kernel speedup across three models (Gemma 27B, Qwen3 32B, and Llama3.3 70B) and up to 1.54×\times end-to-end improvement by leveraging the 12--15×\times latency advantage of shared memory over global memory access. Our optimization reduces instruction counts through simplified indexing logic while using only 64 bytes of shared memory per thread block, demonstrating that lightweight optimizations can deliver substantial performance gains with minimal engineering effort. This work provides a plug-and-play solution for the HuggingFace ecosystem that democratizes access to advanced models on existing GPU infrastructure.

Xiangbo Qi, Chaoyi Jiang, Murali Annavaram

University of Southern California Los Angeles, USA

LLM Inference AccelerationGPU Kernel OptimizationLLM QuantizationNeural Network Quantization
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Apr 2, 2026

AdaHOP: Fast and Accurate Low-Precision Training via Outlier-Pattern-Aware Rotation

Hadamard transforms have become a key tool for stabilizing low-precision training, but existing methods apply them uniformly across tensors and computation paths. We show that this one-size-fits-all strategy is inherently limited: Hadamard smoothing reduces quantization error only when its direction is properly aligned with the operand's outlier structure. Through a systematic study of weights, activations, and gradients in LLM training, we identify three stable outlier patterns, Row-wise, Column-wise, and None, and show that each outlier pattern pair in matrix multiplication requires a distinct transform or outlier-handling strategy. We propose AdaHOP, Adaptive Hadamard transform with Outlier-Pattern-aware strategy, which applies Inner Hadamard Transform (IHT) when inner-dimension mixing properly suppresses the operands' outliers, and selectively applies Outlier Extraction (OE) that extracts dominant outlier rows or columns into a high-precision path when it does not. With fused, hardware-aware Triton kernels, AdaHOP enables training from scratch at MXFP4 precision with BF16-level quality, while achieving up to 3.6X memory compression, 1.46X end-to-end training speedup over BF16.

Seonggon Kim, Alireza Khodamoradi, Pranathi Vasireddy +2

Advanced Micro Devices, Inc. · POSTECH

Walsh-Hadamard TransformLow-Precision TrainingLLM QuantizationQuantization-Aware TrainingMixed-Precision Quantization
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Mar 30, 2026

PolarQuant: Optimal Gaussian Weight Quantization via Hadamard Rotation for LLM Compression

We present PolarQuant, a post-training weight quantization method for large language models (LLMs) that exploits the distributional structure of neural network weights to achieve near-lossless compression. PolarQuant operates in three stages: (1) block-wise normalization to the unit hypersphere, (2) Walsh-Hadamard rotation to transform coordinates into approximately Gaussian random variables, and (3) quantization with centroids matched to the Gaussian distribution. Our ablation reveals that Hadamard rotation alone accounts for 98% of the quality improvement, reducing Qwen3.5-9B perplexity from 6.90 (absmax Q5) to 6.40 (Delta = +0.03 from FP16), making it practically lossless without any calibration data. Furthermore, PolarQuant functions as an effective preprocessing step for downstream INT4 quantizers: PolarQuant Q5 dequantized and re-quantized by torchao INT4 achieves perplexity 6.56 versus 6.68 for direct absmax INT4, while maintaining 43.1 tok/s throughput at 6.5 GB VRAM. Code and models are publicly available.

Caio Vicentino

LLM QuantizationNeural Network QuantizationPost-Training QuantizationWeight-Only Quantization
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Mar 30, 2026

Adaptive Block-Scaled Data Types

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

Jack Cook, Hyemin S. Lee, Kathryn Le +4

Massachusetts Institute of Technology · NVIDIA

Neural Network QuantizationLLM Quantization4-Bit QuantizationPost-Training Quantization
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Mar 30, 2026

ITQ3_S: High-Fidelity 3-bit LLM Inference via Interleaved Ternary Quantization with Rotation-Domain Smoothing

We present ITQ3_S (Interleaved Ternary Quantization -- Specialized), a novel 3-bit weight quantization format for LLMs integrating TurboQuant (TQ), a rotation-domain strategy based on the Fast Walsh-Hadamard Transform (FWHT). Conventional 3-bit methods suffer precision loss from heavy-tailed weight distributions and inter-channel outliers. ITQ3_S pre-rotates the weight space via FWHT before quantization, spreading outlier energy across the vector and inducing a near-Gaussian distribution amenable to uniform ternary coding. We derive a rigorous dequantization procedure fusing a 256-point Inverse FWHT into the CUDA shared-memory loading stage, ensuring reconstruction error is bounded exclusively by the ternary quantization grid with no additional error from the transform inversion. For any weight vector w∈R256\mathbf{w} \in \mathbb{R}^{256}, the reconstruction satisfies ∥w^−w∥2≤εq\|\hat{\mathbf{w}} - \mathbf{w}\|_2 \leq ε_q, strictly smaller than uniform 3-bit baselines that do not exploit rotation-induced distribution normalization. TurboQuant lacks a native CUDA kernel, precluding direct deployment; naively composing TQ with existing weight quantizers introduces domain mismatch errors that accumulate across layers, degrading quality below standard 3-bit baselines. ITQ3_S resolves this by co-designing the FWHT rotation and quantization kernel as a unified pipeline grounded in the IQ3_S weight format, with the inverse transform fused into the CUDA MMQ kernel. Empirically, on the NVIDIA RTX 5090 (Blackwell), ITQ3_S achieves perplexity competitive with FP16 while delivering throughput exceeding 1.5x that of 4-bit alternatives via optimized DP4A and Tensor Core scheduling. Our results establish ITQ3_S as a practical, mathematically grounded solution for high-fidelity LLM deployment on consumer hardware.

Edward J. Yoon

LLM QuantizationTernary QuantizationLLM Inference AccelerationWeight-Only QuantizationRotation-Based Quantization
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Mar 26, 2026

GlowQ: Group-Shared LOw-Rank Approximation for Quantized LLMs

Quantization techniques such as BitsAndBytes, AWQ, and GPTQ are widely used as a standard method in deploying large language models but often degrades accuracy when using low-bit representations, e.g., 4 bits. Low-rank correction methods (e.g., LQER, QERA, ASER) has been proposed to mitigate this issue, however, they restore all layers and insert error-correction modules into every decoder block, which increases latency and memory overhead. To address this limitation, we propose GlowQ, a group-shared low-rank approximation for quantized LLMs that caches a single shared right factor per input-sharing group and restores only the groups or layers that yield the highest accuracy benefit. GlowQ computes the high-precision projection once per input-sharing group and reuses it across its modules, reducing parameter and memory overhead, and retaining the expressivity of layer-specific corrections. We also propose a selective variant, GlowQ-S, that applies the cached shared module only where it provides the largest benefit. Compared with strong baselines, our approach reduces TTFB by (5.6%) and increases throughput by (9.6%) on average, while reducing perplexity on WikiText-2 by (0.17%) and increasing downstream accuracy by 0.42 percentage points. The selective model GlowQ-S further reduces latency, cutting TTFB by (23.4%) and increasing throughput by (37.4%), while maintaining accuracy within 0.2 percentage points on average. Code is available at https://github.com/ahnselim/GlowQ.

Selim An, Il hong Suh, Yeseong Kim

Department of Artificial Intelligence, DGIST, Korea · COGA robotics, Korea · Department of Electrical Engineering, POSTECH, Korea

LLM QuantizationLLM Inference AccelerationLow-Bit Quantization
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Mar 26, 2026

SliderQuant: Accurate Post-Training Quantization for LLMs

In this paper, we address post-training quantization (PTQ) for large language models (LLMs) from an overlooked perspective: given a pre-trained high-precision LLM, the predominant sequential quantization framework treats different layers equally, but this may be not optimal in challenging bit-width settings. We empirically study the quantization impact of different layers on model accuracy, and observe that: (1) shallow/deep layers are usually more sensitive to quantization than intermediate layers; (2) among shallow/deep layers, the most sensitive one is the first/last layer, which exhibits significantly larger quantization error than others. These empirical observations imply that the quantization design for different layers of LLMs is required on multiple levels instead of a single level shared to all layers. Motivated by this, we propose a new PTQ framework termed Sliding-layer Quantization (SliderQuant) that relies on a simple adaptive sliding quantization concept facilitated by few learnable parameters. The base component of SliderQuant is called inter-layer sliding quantization, which incorporates three types of novel sliding window designs tailored for addressing the varying quantization sensitivity of shallow, intermediate and deep layers. The other component is called intra-layer sliding quantization that leverages an incremental strategy to quantize each window. As a result, SliderQuant has a strong ability to reduce quantization errors across layers. Extensive experiments on basic language generation, zero-shot commonsense reasoning and challenging math and code tasks with various LLMs, including Llama/Llama2/Llama3/Qwen2.5 model families, DeepSeek-R1 distilled models and large MoE models, show that our method outperforms existing PTQ methods (including the latest PTQ methods using rotation transformations) for both weight-only quantization and weight-activation quantization.

Shigeng Wang, Chao Li, Yangyuxuan Kang +3

Intel Labs China · BUPT

LLM QuantizationPost-Training QuantizationNeural Network QuantizationWeight-Only QuantizationActivation Quantization
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Mar 24, 2026

APreQEL: Adaptive Mixed Precision Quantization For Edge LLMs

Today, large language models have demonstrated their strengths in various tasks ranging from reasoning, code generation, and complex problem solving. However, this advancement comes with a high computational cost and memory requirements, making it challenging to deploy these models on edge devices to ensure real-time responses and data privacy. Quantization is one common approach to reducing memory use, but most methods apply it uniformly across all layers. This does not account for the fact that different layers may respond differently to reduced precision. Importantly, memory consumption and computational throughput are not necessarily aligned, further complicating deployment decisions. This paper proposes an adaptive mixed precision quantization mechanism that balances memory, latency, and accuracy in edge deployment under user-defined priorities. This is achieved by analyzing the layer-wise contribution and by inferring how different quantization types behave across the target hardware platform in order to assign the most suitable quantization type to each layer. This integration ensures that layer importance and the overall performance trade-offs are jointly respected in this design. Our work unlocks new configuration designs that uniform quantization cannot achieve, expanding the solution space to efficiently deploy the LLMs on resource-constrained devices.

Meriem Bouzouad, Yuan-Hao Chang, Jalil Boukhobza

Lab-STICC, CNRS UMR 6285 , ENSTA, Institut Polytechnique de Paris, Brest, France · National Taiwan University, Taipei, Taiwan

Hardware-Aware QuantizationLLM QuantizationNeural Network QuantizationMixed-Precision QuantizationOn-Device Language Model InferenceLLM Inference Acceleration
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Mar 23, 2026

FAAR: Format-Aware Adaptive Rounding for NVFP4

Deploying large language models (LLMs) on edge devices requires extremely low-bit quantization. Ultra-low precision formats such as NVFP4 offer a promising solution for reducing memory footprint and accelerating computation. However, existing quantization methods typically rely on conventional rounding strategies and fail to account for the non-uniformity of the NVFP4 numerical grid, resulting in suboptimal rounding decisions and amplified quantization errors. To address this, we propose Format-Aware Adaptive Rounding (FAAR), a learnable rounding strategy tailored for the NVFP4 format. Unlike conventional quantization paradigms, FAAR explicitly incorporates the non-uniform NVFP4 grid into the optimization process. By adaptively adjusting rounding decisions guided by loss gradients, our method effectively approximates the theoretically optimal quantization. To complement FAAR, we introduce a 2-stages Format Alignment (2FA) fine-tuning scheme that aligns LLM parameters layer-by-layer to the NVFP4 numerical space, further narrowing the performance gap. Remarkably, this learnable optimization incurs a minimal training overhead of only 4 GPU hours on Llama3-1B. Extensive experiments demonstrate the effectiveness of our approach. Compared with Round-to-Nearest (RTN), our method reduces perplexity on WikiText-2 from 14.28 to 12.60 on Llama3-1B and from 23.06 to 21.27 on Qwen3-1.7B. Additionally, our method consistently outperforms state-of-the-art approaches across various zero-shot downstream tasks.

Hanglin Li, Shuchang Tian, Chen Lin +2

Li Auto Inc.

LLM Quantization4-Bit QuantizationPost-Training Quantization
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Mar 20, 2026

DAQ: Delta-Aware Quantization for Post-Training LLM Weight Compression

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

Xiaoming Yu, Shize Tang, Guanghua Yu +4

Yuanbao & Hunyuan AI Infra Team

QuantizationLLM QuantizationNeural Network QuantizationPost-Training QuantizationWeight-Only Quantization
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Mar 18, 2026

Weight Clustering Reveals the Importance of Relative Rank in Large Language Models

Large language models (LLMs) contain billions of parameters, but many exact weight values are not essential. We apply scalar KK-means clustering to pretrained models, replacing each weight matrix with only 16--64 shared values. For Llama~3.1-8B-Instruct and SmolLM2-135M, this preserves strong accuracy without retraining, providing a simple way to compress LLMs on disk. Fine-tuning only the cluster centroids further recovers 30--40% of the remaining accuracy loss. Using clustering as an analysis tool, we then keep the cluster assignments fixed and perturb only the shared values, to study which of their properties matter most. We find that preserving their relative rank (which connections are stronger or weaker than others) is more important than preserving their exact magnitudes. Breaking this ordering greatly increases perplexity, while changing the values but keeping the ordering causes little loss in many middle and late layers. However, rank preservation alone is not sufficient. Model performance also depends on maintaining the variance of the reconstructed weights, while early layers remain more sensitive; perturbing the cluster assignments themselves shows that their spatial geometry is also load-bearing. We observe the same behavior across four LLMs from two architecture families. These results suggest that the ordering of weights, together with their overall variance, plays a central role in LLM compression and robustness.

Borja Aizpurua, Sukhbinder Singh, Román Orús

Multiverse Computing, San Sebasti´an, Spain · Department of Basic Sciences, Tecnun - University of Navarra, San Sebasti´an, Spain · Multiverse Computing, Toronto, Ontario, Canada +2

LLM CompressionLLM QuantizationClustering
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Mar 18, 2026

RAMP: Reinforcement Adaptive Mixed Precision Quantization for Efficient On Device LLM Inference

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.

Arpit Singh Gautam, Saurabh Jha

LLM QuantizationNeural Network QuantizationLLM Inference EfficiencyMixed-Precision QuantizationPost-Training Quantization
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Mar 17, 2026

Understanding Quantization of Optimizer States in LLM Pre-training: Dynamics of State Staleness and Effectiveness of State Resets

Quantizing optimizer states is becoming an important ingredient of memory-efficient large-scale pre-training, but the resulting optimizer dynamics remain only partially understood. We study low-precision exponential moving average (EMA) optimizer states and show how quantization can cause many nominal updates to round back to the same stored value, making the state effectively stale and slowing adaptation beyond what the nominal decay would suggest. We then develop a simple predictive model of stalling that estimates one-step stalling probabilities and characterizes how stalling builds up over time after the initialization. This perspective provides a mechanistic explanation for why optimizer-state resets help in low precision: once a quantized EMA becomes effectively stale, resetting it can temporarily restore responsiveness. Motivated by this picture, we derive a simple theory-guided method for choosing useful reset periods, showing that in low precision the key question is not only whether resets help, but when they should be applied. Experiments in controlled simulations and LLM pre-training show that suitable reset schedules recover the performance lost to low-precision state storage while substantially reducing optimizer-state memory.

Kristi Topollai, Anna Choromanska

New York University

Low-Precision TrainingLow-Bit QuantizationMemory-Efficient TrainingNeural Network QuantizationLLM Quantization
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Mar 17, 2026

BATQuant: Outlier-resilient MXFP4 Quantization via Learnable Block-wise Optimization

Microscaling floating-point (MXFP) formats have emerged as a promising standard for deploying Multi-modal Large Language Models (MLLMs) and Large Language Models (LLMs) on modern accelerator architectures. However, existing Post-Training Quantization (PTQ) methods, particularly rotation-based techniques designed for integer formats, suffer from severe performance collapse when applied to MXFP4. Recent studies attribute this failure to a fundamental format mismatch: global orthogonal rotations inadvertently transfer outlier energy across quantization blocks, inducing new outliers that disrupt local block-wise scaling, while often creating bimodal activation distributions that underutilize the limited quantization range. To address these issues, we propose BATQuant (Block-wise Affine Transformation), which restricts transformations to align with MXFP granularity to prevent cross-block outlier propagation, while relaxing orthogonality constraints to optimize distribution shaping. To ensure parameter efficiency, we introduce Global and Private Kronecker (GPK) decomposition to effectively reduces storage and runtime overhead and incorporate Block-wise Learnable Clipping to suppress residual outliers. Extensive experiments on both MLLMs and LLMs demonstrate that BATQuant establishes new state-of-the-art results under aggressive W4A4KV16 configurations, recovering up to 96.43% of full-precision performance on multimodal benchmarks and clearly outperforming existing methods across diverse tasks.

Ji-Fu Li, Manyi Zhang, Xiaobo Xia +4

Huawei Technologies · University of Science and Technology of China

LLM QuantizationNeural Network QuantizationPost-Training QuantizationVLM Quantization
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Mar 17, 2026

Frequency Matters: Fast Model-Agnostic Data Curation for Pruning and Quantization

Post-training model compression is essential for enhancing the portability of Large Language Models (LLMs) while preserving their performance. While several compression approaches have been proposed, less emphasis has been placed on selecting the most suitable set of data (the so-called calibration data) for finding the compressed model configuration. The choice of calibration data is a critical step in preserving model capabilities both intra- and inter-tasks. In this work, we address the challenge of identifying high-performance calibration sets for both pruning and quantization by analyzing intrinsic data properties rather than model-specific signals. We introduce ZipCal, a model-agnostic data curation strategy that maximizes lexical diversity based on Zipfian power laws. Experiments demonstrate that our method outperforms standard uniform random sampling across various pruning benchmarks. Notably, it also performs on par, in terms of downstream performance, with a state-of-the-art method that relies on model perplexity. The latter becomes prohibitively expensive for large-scale models and datasets, while ZipCal is on average ∼\sim240×\times faster due to its tractable linear complexity. We make the code and the experiments available at https://github.com/FrancescoMonaco/ZipCal.

Francesco Pio Monaco, Elia Cunegatti, Flavio Vella +1

University of Trento

LLM CompressionLLM PruningLLM QuantizationPost-Training Quantization
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Mar 12, 2026

Adapting Methods for Domain-Specific Japanese Small LMs: Scale, Architecture, and Quantization

This paper presents a systematic methodology for building domain-specific Japanese small language models using QLoRA fine-tuning. We address three core questions: optimal training scale, base-model selection, and architecture-aware quantization. Stage 1 (Training scale): Scale-learning experiments (1k--5k samples) identify n=4,000 as optimal, where test-set NLL reaches minimum (1.127) before overfitting at 5k samples. Stage 2 (Compare finetuned SLMs): Comparing four Japanese LLMs shows that Llama-3 models with Japanese continual pre-training (Swallow-8B, ELYZA-JP-8B) outperform multilingual models (Qwen2.5-7B). Stage 3 (Quantization): Llama-3 architectures improve under Q4_K_M quantization, while GQA architectures degrade severely (Qwen2.5: -0.280 points). Production recommendation: Swallow-8B Q4_K_M achieves 2.830/3 score, 8.9 s/question, 4.9 GB size. The methodology generalizes to low-resource technical domains and provides actionable guidance for compact Japanese specialist LMs on consumer hardware.

Takato Yasuno

Language ModelingSmall Language ModelsLLM Fine-TuningDomain Adaptation for LLMsLLM Quantization
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Mar 11, 2026

Leech Lattice Vector Quantization for Efficient LLM Compression

Scalar quantization of large language models (LLMs) is fundamentally limited by information-theoretic bounds. While vector quantization (VQ) overcomes these limits by encoding blocks of parameters jointly, practical implementations must avoid the need for expensive lookup mechanisms or other explicit codebook storage. Lattice approaches address this through highly structured and dense packing. This paper explores the Leech lattice, which, with its optimal sphere packing and kissing configurations at 24 dimensions, is the highest dimensional lattice known with such optimal properties. To make the Leech lattice usable for LLM quantization, we extend an existing search algorithm based on the extended Golay code construction, to i) support indexing, enabling conversion to and from bitstrings without materializing the codebook, ii) allow angular search over union of Leech lattice shells, iii) propose fully-parallelisable dequantization kernel. Lastly, we provide a geometric reinterpretation of combining shape--gain quantization with GPTQ-style Hessian corrections: the standard scale-correction step of shape--gain acts as a retraction onto a product of spheres, yielding a Spherical GPTQ primarily acting on directions. We find that low-angular-distortion LLVQ reduces sensitivity to Hadamard/rotation preprocessing, and enables a strong Hadamard-free PTQ in practice. LLVQ delivers state-of-the-art LLM quantization performance, outperforming recent methods such as Quip#, QTIP, and PVQ. The results highlight the effectiveness of high-dimensional lattices for scalable, theoretically grounded model compression.

Tycho F. A. van der Ouderaa, Mart van Baalen, Paul Whatmough +1

Qualcomm AI Research

LLM QuantizationLLM CompressionVector QuantizationPost-Training Quantization
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Mar 11, 2026

The Curse and Blessing of Mean Bias in FP4-Quantized LLM Training

FP4 training promises substantial memory and compute savings for large language models, but remains fragile because blockwise quantization is dictated by extreme activation magnitudes, which inflate dynamic range and compress long-tail signals. We identify a counterintuitive source of this failure: dominant activation outliers are not merely arbitrary sparse events, but are largely induced by a coherent rank-one mean bias, whose direction aligns with the leading anisotropic spectral component. This mean component strengthens during training, is amplified and reshaped by attention and FFN operators, and increasingly dominates top activation magnitudes. Crucially, this discovery reveals that a seemingly complex outlier-suppression problem admits a truly simple solution: isolate the coherent mean before quantization. We therefore propose Averis, a mean-residual splitting quantization method that separates the mean component using only reductions and elementwise subtractions before FP4 quantization. Across Qwen3 0.6B Dense trained on 100B tokens and Qwen3 7B A1.5B MoE trained on 50B tokens, Averis enables robust W4A4G4 FP4 training, reducing BF16 loss gaps to 1.19%/0.81% versus 2.05%/1.10% for NVIDIA's recently released Hadamard-based outlier-smoothing method, while limiting downstream gaps to 0.89/0.71 points. With only 2.20% end-to-end overhead over vanilla NVFP4, about 30% of NVIDIA's Hadamard-based design, Averis provides a hardware-efficient path to stable low-bit LLM training. Complementary to Hadamard, Averis further reduces the Qwen3-0.6B loss and downstream gaps to 0.94% and 0.73 points when combined. Code is available at: https://anonymous.4open.science/r/averis-504D.

Hengjie Cao, Zhendong Huang, Mengyi Chen +15

Fudan University · Shanghai Innovation Institute · University of Bath +5

LLM Quantization4-Bit QuantizationActivation QuantizationQuantization-Aware TrainingActivation Outliers
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Mar 11, 2026

TTQ: Activation-Aware Test-Time Quantization to Accelerate LLM Inference On The Fly

To tackle the huge computational demand of large foundation models, activation-aware compression techniques without retraining have been introduced. However, since these methods highly rely on calibration data, domain shift issues may arise for unseen downstream tasks. We propose a test-time quantization (TTQ) framework which compresses large models on the fly at inference time to resolve this issue. With an efficient online calibration, instant activation-aware quantization can adapt every prompt regardless of the downstream tasks, yet achieving inference speedup. Several experiments demonstrate that TTQ can improve the quantization performance over state-of-the-art baselines.

Toshiaki Koike-Akino, Jing Liu, Ye Wang

Mitsubishi Electric Research Laboratories (MERL), 201 Broadway, Cambridge, MA 02139, USA

LLM QuantizationNeural Network QuantizationLLM Inference AccelerationActivation Quantization
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