Weight-Only Quantization

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15 papers in the last four weeks, up 200% on the four weeks before. 0.1% of all new papers.

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Latest papers 55

Jul 8, 2026cs.LG

KronQ: LLM Quantization via Kronecker-Factored Hessian

Post-training quantization (PTQ) is a widely adopted technique for compressing large language models (LLMs) without retraining. Existing second-order PTQ methods, including GPTQ, construct quantization objectives exclusively from input activation statistics, effectively assuming that all output channels contribute equally to the layer-wise reconstruction objective. We propose KronQ, a PTQ framework that challenges this assumption by introducing the gradient covariance into the quantization pipeline. Under the Kronecker-factored Hessian approximation, the quantization loss depends jointly on both the activation and gradient covariances, and KronQ exploits this at two complementary levels. (1) KronQ introduces bidirectional incoherence processing, extending the existing input-side random rotation to the output dimension using the gradient covariance, reducing weight magnitude variance across both input and output dimensions. (2) KronQ derives a new sensitivity metric for inter-layer mixed-precision allocation, driven by the gradient and activation Hessian traces. Notably, in the case of 2-bit weight-only quantization on LLaMA-3-70B, while GPTQ and GPTAQ diverge or produce degenerate quantizations (>2000 perplexity on WikiText-2), KronQ achieves 7.93 perplexity.

Donghyun Lee, Yuhang Li, Ruokai Yin +1

University of Southern California · Yale University

Mixed-Precision Quantization LLM Quantization Rotation-Based Quantization Weight-Only Quantization Post-Training Quantization Neural Network Quantization

Jul 1, 2026math.OC

Boundary-Aware Quantization: Finite-Scale Decision Geometry of Neural Classifiers

We measured quantization-induced decision-boundary changes using local logit-margin radii, first-order boundary displacement, normal variation, slice-boundary Jaccard distance, grid prediction changes, multiclass junction counts, and low-margin boundary-band flips. On the digits benchmark, 8-bit weight quantization preserved all test labels while producing boundary-mask Jaccard

0.428

on the PCA slice; at 4 bits, accuracy remained

0.9733

, while boundary Jaccard rose to

0.970

and median local boundary shift reached

0.0290

. Interpolation between adjacent quantization levels localized the visible reconfigurations at multiclass junctions, with 12, 34, and 17 triple-junction cells in the selected transitions. Calibration-to-test stopping reduced the digits held-out flip rate from

0.0094

to

0.0022

and boundary Jaccard from

0.825

to

0.524

; the same stopping rule also reduced flips on MNIST and Fashion-MNIST. On official CIFAR-10 subsets, PTQ-W selected by accuracy gave 6-bit flip

0.0367

and boundary Jaccard

0.184

, whereas boundary-aware stopping selected 8-bit flip

0.0083

and boundary Jaccard

0.048

. On full CIFAR-10 with three seeds, 6-bit PTQ-W lost

0.0029

accuracy relative to float, changed

5.3\%

of held-out decisions, and changed

24.5\%

of low-margin boundary-band decisions. A fixed-bit boundary-gap rounding term changed the trade-off at 4 bits by reducing boundary Jaccard from

0.457

to

0.435

and boundary-band pair-order flip from

0.3600

to

0.3558

, with an accuracy trade-off; the 3-bit stress test exposed the tuning limit of this surrogate. Calibration boundary Jaccard predicted held-out boundary Jaccard across PTQ-W and optimized rounding variants with

r=0.947

--

0.994

.

O. M. Kiselev

Innopolis University, Innopolis, Republic of Tatarstan, Russian Federation

Weight-Only Quantization Post-Training Quantization Neural Network Quantization

Jun 26, 2026stat.ML

Spectral Perturbation of the Empirical Fisher Information Matrix under Weight Quantization

We study the spectral perturbation of the empirical Fisher Information Matrix (FIM) of a parametric statistical model under two structured perturbations: departure of the input from a reference (in-distribution) ensemble, and finite-precision (quantized) perturbation of the model's parameters. For the first, under an explicit local curvature-monotonicity hypothesis on the dominant eigenvalue lambda_max of the FIM, we show departure from a reference manifold provably elevates lambda_max relative to a calibration baseline (Proposition 3.2), and discuss why this hypothesis is required, since curvature need not increase monotonically under every perturbation. Our principal result is a directional eigenvalue perturbation bound, via Weyl's inequality, showing lambda_max under a quantization noise perturbation is lower bounded by its unperturbed value up to a third-order remainder, and, under a mild genericity condition, strictly exceeds it at leading order (Theorem 4.3). We give two tractable approximations to lambda_max -- one heuristic, one with a rigorous two-sided bound -- and a completeness result for a threshold-based partition of an augmented state space. These results motivate using sigma_t = lambda_max(F_t)/lambda_base as a runtime monitoring statistic for deployed language models: the quantization result offers a mechanism for an empirical observation of our own, where a calibration threshold for this statistic was approximately 244 times larger than a preliminary full-precision estimate on a 4-bit quantized model, a single measurement rather than a value derived in closed form. We report supporting measurements (twelve models, n=1,080 trajectories) broadly consistent with our predictions, discuss the scope and limitations of every result, and state as an open problem the closed-form prediction of the quantization inflation magnitude our bound does not supply.

Rahid Zahid Alekberli, Hikmat Karimov

Institute of Defense Technologies and Cybersecurity, Azerbaijan Technical University, Baku, Azerbaijan

Information Geometry Weight-Only Quantization Fisher Information

Jun 22, 2026cs.LG

GRINQH: Graded Input-based Quantization Hierarchy for Efficient LLM Generation

Autoregressive decoding with LLMs is primarily bottlenecked by GPU memory bandwidth, especially in edge-computing settings. While quantization is essential for mitigating this bottleneck, most existing methods treat inference as a uniform process and fail to account for the asymmetry between the compute-bound prefill stage and the memory-bound decoding stage. We propose GRINQH (GRaded INput-based Quantization Hierarchy), a weight-only post-training quantization framework that accelerates decoding by unifying quantization and sparsification. GRINQH leverages activation magnitudes as a proxy for computational importance to dynamically assign weight channels to different precision levels, enabling flexible average bit widths during decoding. Evaluated on Llama3 and Qwen3 models, GRINQH outperforms state-of-the-art fixed- and mixed-precision baselines at comparable 3- and 4-bit settings, even enabling effective 2-bit generation. We experimentally verify theoretical speedups by leveraging a hierarchical nested memory layout for multi-precision storage in a custom GPU kernel. Ultimately, GRINQH establishes a new state-of-the-art Pareto frontier for LLM generation, enabling a dynamic trade-off between generation quality and inference speed.

Jette Oberländer, Jan Finkbeiner, Catherine M. Schöfmann +1

Fakultät für Informatik, RWTH Aachen, Aachen, 52074, Germany · Peter Grünberg Institut, Forschungszentrum Jülich GmbH, Jülich, 52425, Germany · Fakultät für Elektrotechnik und Informationstechnik, RWTH Aachen, Aachen, 52062, Germany

Mixed-Precision Quantization LLM Quantization LLM Inference LLM Inference Acceleration Weight-Only Quantization Post-Training Quantization

Jun 20, 2026cs.LG

On the Expressive Power of Weight Quantization in Large Language Models

In recent years, weight quantization that encodes the learnable parameters of large language models in an

n

-bit format has garnered significant attention due to its potential for model compression and inference acceleration. Many practical techniques have been developed; however, the theoretical understanding of many aspects, especially the approximation and degradation of expressive power as the number of quantization bits decreases, remains unclear. In this paper, we provide a theoretical investigation into the expressive capability of large language models relative to the number of quantization bits. We argue that 1.58-bit is the limiting precision for weight quantization by establishing the universal approximation and expressive collapse properties of weight-quantized models with respect to the number of quantization bits. Additionally, we confirm that weight quantization leads to expressive degradation, in which the expressive capacity of weight-quantized models degrades polynomially as the number of quantization bits decreases. These theoretical findings provide a solid foundation for advancing weight quantization in the context of scaling laws and shed insights for future research in model compression and inference acceleration.

Shao-Qun Zhang

National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210063, China. · School of Intelligent Science and Technology, Nanjing University, Suzhou 215163, China.

LLM Quantization Weight-Only Quantization Neural Network Expressivity Low-Bit Quantization

Jun 14, 2026cs.LG

MosaicQuant: Inlier-Outlier Disaggregation for Unified 4-Bit LLM Quantization

4-bit quantization significantly reduces the memory footprint and accelerates the inference of large language models (LLMs). However, its limited bit-width representation struggles to faithfully capture both dense common values (\emph{inliers}) and rare large-magnitude values (\emph{outliers}), causing substantial accuracy degradation. Existing mixed-precision methods mitigate this by retaining outliers in high precision, but at the cost of breaking the uniformity of low-bit execution, introducing precision conversion and extra data movement that undermine practical speedup. We propose \textbf{MosaicQuant}, a unified 4-bit LLM quantization paradigm built on a novel principle of \emph{inlier--outlier disaggregation}. Rather than elevating outlier precision, MosaicQuant quantizes the full weight matrix into a dense 4-bit base component, where inliers are captured faithfully while outlier are inevitably quantized. A sparse 4-bit residual component is then introduced to compensate for these quantization errors, selectively targeting the most error-critical weight blocks where output distortion is shown to be concentrated. However, a unified representation alone is insufficient, as naïvely executing the sparse residual as a separate kernel still breaks the unified low-bit inference pipeline. To bridge this gap, we introduce \textbf{ZipperEngine}, which fuses sparse block computation into the dense 4-bit GEMM kernel via an overlapped pipeline, unifying not only the representation but also the execution into a single coherent low-bit inference pipeline. Extensive experiments on LLaMA3 and Qwen3 demonstrate that MosaicQuant preserves near-FP16 accuracy while achieving up to

1.24\times

speedup over the W16A16 baseline.

Yangjia Hu, Haodong Wang, Zicong Hong +8

HKUST · EPFL · MetaX Integrated Circuits Co., Ltd

LLM Quantization 4-Bit Quantization LLM Inference Acceleration Weight-Only Quantization Neural Network Quantization

Jun 12, 2026cs.LG

Signed Symmetric Quantization for Few-Bit Integers

The signed integer alphabet contains one more negative representable value than positive. Yet, by convention, the standard symmetric integer quantizer fixes its scale to be strictly positive, which assigns this extra representable value to the negative tail and can force clipping of positive outliers. In this work, we show that, at few-bit precision, such clipping is a non-trivial source of quantization error. Asymmetric quantization addresses this problem with a zero point, shifting the grid toward the observed data range; however, this flexibility is well-known to carry a runtime penalty. For example, in llama.cpp on an AMD EPYC(TM) "Turin" CPU, a 4-bit symmetric format uses up to 9% less memory with up to 2.45

\times

higher throughput than its asymmetric counterpart. We highlight signed symmetric quantization as a third option that retains the runtime profile of symmetric quantization without the penalty of the asymmetric format: our signed absmax grid places the extra representable value on the dominant-outlier tail through a principled and lightweight sign selection rule while keeping the zero point at zero. Our theoretical analysis offers two main results. First, we establish the signed absmax grid as conditionally bound-optimal on

\ell_2

quantization error, and show that the condition holds for 88-99% of weight groups across pre-trained large language models (LLMs) at low bit widths. Second, we show that negating the scale of a standard symmetric quantizer is analytically equivalent to a unit zero point shift on the same signed integer alphabet. We empirically validate our proposal on models from the Qwen3, Qwen3.5, and Llama3 families, and observe improvement in perplexity and downstream few-shot accuracy over the standard unsigned symmetric quantizer at no extra inference cost

Ian Colbert, Eashan Dash, Pablo Monteagudo-Lago +5

AMD

LLM Quantization Weight-Only Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Jun 11, 2026cs.LG

Multi-Bitwidth Quantization for LLMs Using Additive Codebooks

As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the trade-off between performance and efficiency without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework that enables inference-time precision control over LLM weights from a single trained model. Our method is theoretically grounded in information theory and successive refinement. We establish that LLM weights, which commonly follow a Gaussian distribution, can be optimally reconstructed with increasing fidelity as additional bits are incorporated, under a weighted mean squared error distortion motivated by LLM loss functions. To realize this in practice, Drop-by-Drop incorporates Matryoshka-style supervision into the loss function, exploiting the structure of additive codebooks. Drop-by-Drop produces a single model where ordered subsets of codebooks yield accurate partial reconstructions at each precision level. This approach significantly reduces storage and memory overhead by allowing a single checkpoint to serve multiple bitwidths, while maintaining competitive perplexity and accuracy across major architectures, such as Qwen, LLaMA, Gemma, and Mistral.

Liza Babaoglu, Shuangyi Chen, Ashish Khisti

University of Toronto

LLM Quantization Weight-Only Quantization Iterative Refinement Post-Training Quantization Neural Network Quantization

Jun 9, 2026cs.LG

Optimal Post-Training Quantization Scales and Where to Find Them

Post-training quantization (PTQ) compresses large language models by mapping weights to low-bit representations. The scaling factor that defines the quantization grid is typically chosen using simple, data-free heuristics. In this work, we present PiSO (Piecewise Scale Optimization), an algorithm that leverages calibration data to compute the optimal channel-wise weight scales exactly and efficiently under round-to-nearest quantization. PiSO partitions the scale search space into finitely many intervals on which the objective admits a closed-form minimizer. We extend PiSO to group-wise quantization via principled heuristics and propose effective strategies for interleaving scale optimization with error correction. Experiments on Llama and Qwen models across multiple model sizes and target weight bit-widths demonstrate consistent improvements in perplexity and downstream zero-shot accuracy, both standalone and combined with error correction. In particular, we observe increased benefits as the target bit-width narrows and quantization becomes more challenging.

Juan Amboage, Pablo Monteagudo-Lago, Ian Colbert +2

AMD

LLM Quantization Weight-Only Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Jun 3, 2026cs.AI

Minimizing the Hidden Cost of Scales: Graph-Guided Ultra-Low-Bit Quantization for Large Language Models

Post-training quantization (PTQ) is critical for the efficient deployment of large language models (LLMs). Recent ultra-low-bit PTQ methods rely on rigid weight-saliency assumptions or position heuristics, introducing substantial hidden scaling overhead. We propose SAGE-PTQ (Saliency-Aware Graph-guided Efficient PTQ), a novel ultra-low-bit quantization framework for LLMs that minimizes hidden scaling cost. SAGE-PTQ separates salient and unsalient weights using distributional statistics, then models subsampled unsalient weights as a sparse graph to estimate the optimal number of groups per layer. SAGE-PTQ applies dual-mode quantization, assigning multi-bit precision to salient weights and binarizing unsalient weights. To reduce scaling overhead, SAGE-PTQ uses one per-channel scale for salient weights and one scalar per unsalient group. Finally, SAGE-PTQ implements adaptive saliency thresholding to select the optimal saliency ratio per matrix. SAGE-PTQ achieves 1.03 weight bits and only 0.004 scaling bits per matrix on average, outperforming state-of-the-art methods such as BiLLM and PB-LLM. On LLaMA-3-8B, SAGE-PTQ achieves 6.74 WikiText2 perplexity, compared to 55.8 for BiLLM, while using less than 50% of BiLLM's GPU memory. On LLaMA-2-70B, SAGE-PTQ provides 1.5x faster decoding on one NVIDIA L40 GPU, demonstrating practical inference efficiency.

Rayyan Abdalla, Amir Hussein, Min Wu +1

LLM Quantization LLM Inference Acceleration Weight-Only Quantization Post-Training Quantization Low-Bit Quantization

Jun 2, 2026cs.LG

LiftQuant: Continuous Bit-Width LLM via Dimensional Lifting and Projection

Existing quantization methods are fundamentally limited by rigid, integer-based bit-widths (e.g., 2, 3-bit), resulting in a

deployment gap" where Large Language Models cannot be optimally fitted to specific memory budgets. To bridge this gap, we introduce LiftQuant, a novel framework that enables continuous bit-width control for true Pareto-optimal deployment. The core innovation is a

lift-then-project" mechanism which approximates low-dimensional weight vectors by projecting a simple 1-bit lattice from a higher-dimensional ``lifted" space. Crucially, the effective bit-width is determined simply by the ratio of the lifted dimension to the original dimension, which allows the bit-width to be tuned quasi-continuous as the dimension is a flexible structural parameter. This projection generates a structured yet non-uniform codebook, capturing the expressive power of Vector Quantization (VQ). While beneficial over VQ, LiftQuant's decoding path relies solely on linear transformations and 1-bit uniform quantizers, retaining hardware-friendly nature. This flexibility is transformative: LiftQuant enables a 70B LLM to be compressed to 2.4 bits to precisely fit a 24GB GPU, where its performance significantly surpasses state-of-the-art 2-bit models fitted on the same device. Our code and ckpt is available at https://github.com/Heliulu/LiftQuant.

Liulu He, XuanAng Liu, Juntao Liu +8

Nanjing University, China · China Mobile Research Institute, China · Xiaomi Corporation, China +2

LLM Quantization LLM Compression Weight-Only Quantization Low-Bit Quantization Neural Network Quantization

May 28, 2026cs.AI

LFQ: Logit-aware Final-block Quantization for Boosting the Generation Quality of Low-Bit Quantized LLMs

As large language models continue to scale, low-bit weight-only post-training quantization (PTQ) offers a practical solution to their memory-efficient deployment. Although block-wise PTQ is capable of matching the full-precision (FP) baseline on basic language modeling and understanding, its quality is degraded for generative tasks -- especially at longer responses and extended chains of thought, which is critical in boosting task accuracy. We attribute this shortfall to two factors: (i) the omission of the unembedding layer (the LM head) in block-wise optimization and (ii) the reliance on the mean squared error (MSE) objective. Both factors cause the token probability distribution of the quantized model to misalign with that of the FP model, yielding notable accuracy drops on text generation benchmarks. To rectify the discrepancy, we introduce Logit-aware Final-block Quantization (LFQ), a simple yet effective enhancement to block-wise PTQ that quantizes the final Transformer block by minimizing the cross-entropy between the logits of the FP model and those of its quantized counterpart. By aligning token probabilities at the logit level in the final block, LFQ consistently improves the accuracy of complex generation tasks over state-of-the-art block-wise PTQ across diverse model families, while maintaining parity with FP baselines on language modeling and understanding.

Jung Hyun Lee, June Yong Yang, Jungwook Choi +1

Kim Jaechul Graduate School of AI, KAIST, Daejeon, South Korea · LG AI Research, Seoul, South Korea · Hanyang University, Seoul, South Korea +1

LLM Quantization Weight-Only Quantization Post-Training Quantization Neural Network Quantization Text Generation

May 28, 2026cs.AI

BitTP: The Lightweight Trajectory Prediction Model with BitLLM for Edge-Devices

Trajectory prediction is a fundamental task for autonomous systems, requiring complex reasoning about multi-agent interactions and intents. Large language models (LLMs) have recently been adopted for this task, as they provide strong contextual reasoning and interpretable, language-based trajectory representations. However, these LLM-based predictors are extremely memory- and compute-intensive, making them difficult to deploy on resource-constrained edge devices such as on-board computers in autonomous robots. To bridge this gap, we propose BitTP, which converts an LLM-based trajectory predictor into a lightweight bitlinear architecture. We demonstrate that weight-only quantization to 1.58-bit (BitTP-Weight) is optimal. Crucially, activations must remain in full precision, as quantizing them leads to severe degradation and instability in spatio-temporal reasoning. Empirically, BitTP-Weight not only preserves but improves prediction quality over the full-precision (BF16) LLM baseline, reducing ADE by 14.29% and FDE by 20.97% on average, while simultaneously reducing memory usage and inference latency relative to other quantization methods. These results demonstrate that carefully designed quantization acts as an effective regularizer, enabling the practical deployment of sophisticated LLM-based reasoning on edge devices. Code is available at: https://github.com/MintCat98/BitTP.

Mincheol Kang, Hyunjin Lim, Bomin Kang +1

1KAIST, Republic of Korea · 2DGIST, Republic of Korea

Multi-Agent Trajectory Prediction Weight-Only Quantization Trajectory Prediction Low-Bit Quantization On-Device Inference

May 25, 2026cs.LG

QAM-W: Joint 2D Codebook Quantization for LLM Weights via Hadamard Rotation and Activation-Aware Scaling

Scalar post-training quantizers discard pairwise coordinate structure within weight rows. We introduce QAM-W (Quadrature Amplitude Modulation for Weights), a codec that recovers this structure: each row is L2-normalized, block-Hadamard rotated, paired into 2D coordinates, and quantized against a single Lloyd-Max codebook trained on the unit circular Gaussian, with activation-aware per-channel scaling. In a cross-model study spanning five LLMs from four families (1.1B--13B parameters) and eight quantized configurations, the activation-aware variant at

\approx 5.5

bpw stays within

\pm 0.4\%

of BF16 WikiText-2 perplexity on every model, matching the SmoothQuant W8A8 quality envelope at

32\%

fewer weight bits. Joint 2D coding outperforms polar (amplitude

\times

phase) coding by 2--15pp $Δ$ PPL at equal bitrate, and paired KL against BF16 tracks $Δ$ PPL% at Spearman $ρ= 0.99$ across 37 (method, model) rows, consistent with a monotone composite bound from codec distortion to KL divergence. A 3.5bpw variant is competitive on quantization-tolerant architectures. At strict 4~~bpw, the rotated-codebook frontier method QTIP outperforms QAM-W; the contribution is the quality-preserving 5--6~~bpw band.

Preetam Sharma, Kacper Dobek

Independent Research · Institute of Computing Science Poznan University of Technology, Poznan, Poland

LLM Quantization Rotation-Based Quantization Vector Quantization Weight-Only Quantization Post-Training Quantization

May 24, 2026cs.LG

Influence-Inspired Spectral Rotations for Extreme Low-Bit LLM Quantization

We apply the influence-adaptive Walsh geometry of a companion theory paper (arXiv:2605.01637) to extreme low-bit weight-only LLM quantization. The recipe is one math-invariant transformation: WHT-rotate each linear layer's weight matrix and rescale its columns by per-coordinate Walsh-basis activation energy before handing off to a reconstruction-error quantizer (Intel auto-round). This biases per-group integer rounding toward high-spectral-energy channels. On four pretrained decoder-only models from 135M to 1.5B parameters, BBT-spectral reduces wikitext-2 perplexity by 15-58% relative to vanilla auto-round at W2A16; we also report a TinyLlama-1.1B auxiliary data point. Three extensions transfer the recipe to families it failed on: a per-head PCA matrix-Gamma replacement of q_norm/k_norm for Qwen3 attention (PPL 136.76 -> 88.99 on Qwen3-0.6B); an SO(2) per-pair rotation that commutes with RoPE (PPL 36.93 -> 21.84 on Qwen2.5-1.5B); and an MoE-aware input-side absorption fix identified by architectural fuzzing of Laguna-style fused-expert layouts. A W2-vs-W4 ablation gives a deliberate negative control: the redistribution payoff falls within the +/-0.5 PPL noise floor at W4, consistent with the Schur-convexity intuition that the cost of unconcentrated influence vanishes as the noise budget shrinks. All quantized weights export to OpenVINO IR and run on Intel NPU + Arc dGPU + CPU with PPL invariant to device within +/-0.1. We do not claim a formal Boolean-to-real-valued transfer of the theory paper's majorization argument: the WHT activation energy used here is not the Boolean influence of the theory paper, the link is intuitive, and the contribution is engineering value rather than a transferred theorem. Head-to-head benchmarks against SpinQuant, QuaRot, QuIP-sharp, AQLM, OmniQuant, and ButterflyQuant at matched calibration are the main future-work item.

Gorgi Pavlov

Lehigh University

LLM Quantization Rotation-Based Quantization Weight-Only Quantization Low-Bit Quantization Neural Network Quantization

May 23, 2026cs.CV

Motion-Compensated Weight Compression

Neural network weights are increasingly a bottleneck for deployment, yet most compression pipelines treat layers independently and overlook cross-layer redundancy induced by function-preserving symmetries. We propose Motion-Compensated Weight Compression (MCWC), a weight-only codec that aligns permutation-symmetric blocks (e.g., hidden units and attention heads) to maximize cross-layer correspondence, turning depth into a predictable sequence. In the aligned coordinate system, MCWC uses a lightweight layer-sequential predictor with periodic keyframes and encodes only quantized prediction residuals using a learned entropy model trained under a rate distortion objective. A simple decoder reconstructs deployable weights by entropy decoding, dequantization, predictor-driven reconstruction, and inverse alignment, enabling fast weight materialization for inference. Across Transformer language modeling and vision classification, MCWC improves the rate accuracy Pareto frontier over strong quantization and learned weight-codec baselines, while maintaining competitive decode time. Ablations confirm that alignment, prediction, entropy modeling, and keyframe scheduling are each necessary for the full gains. Our code is available via https://github.com/Ism-ail11/MCWC.

Ismail Lamaakal

Multidisciplinary Faculty of Nador · Mohammed Premier University · Oujda 60000, Morocco

Predictive Coding Weight-Only Quantization Neural Network Compression

May 22, 2026cs.AR

EVA: Accelerating LLM Decoding via an Efficient Vector Quantization Architecture

Large Language Models (LLMs) have achieved impressive performance across diverse domains but remain inefficient during the autoregressive decoding phase. Unlike the prefill stage, which employs compute-bound GEMM operations, decoding executes a sequence of small GEMV-like computations that are memory-bound and underutilize modern accelerators. Weight-only vector quantization (VQ) has emerged as an effective compression technique that clusters model weights into a shared codebook and replaces the original weight matrix with low-precision indices, enabling 2-bit-level weight compression. While this approach substantially reduces model size and memory bandwidth, it still suffers from two critical inefficiencies: the low utilization of GEMV computation and frequent memory conflicts during codebook lookups. This paper presents EVA, an efficient vector-quantization-based architecture that addresses both computational and memory bottlenecks in LLM decoding. EVA builds on a simple yet effective insight that combines input-codebook computation with conflict-free memory access. Instead of reconstructing quantized weights from indices, EVA directly performs dot products between input vectors and the weight codebook, transforming LLM decoding from GEMV to GEMM computation. It then performs structured lookups from an intermediate output buffer, eliminating memory bank conflicts. We further design a hardware-software co-optimized architecture specialized for LLM decoding while remaining compatible with conventional prefill execution. Evaluations show that EVA achieves up to 11.17

\times

speedup and 7.17

\times

higher energy efficiency compared with the SOTA lookup-based architecture, while preserving arithmetic precision after vector quantization. Our code is available at https://github.com/dbw6/Eva.git.

Bowen Duan, Cong Guo, Chiyue Wei +8

Duke University, USA

Vector Quantization LLM Inference Acceleration Weight-Only Quantization Hardware-Software Co-Design Autoregressive Decoding

May 14, 2026cs.LG

A Hardware-Aware, Per-Layer Methodology for Post-Training Quantization of Large Language Models

Scaled Outer Product (SOP) is a post-training quantization methodology for large language model weights, designed to deliver near-lossless fidelity at 4.5--6 bits per weight on hardware with per-layer LUT decode. The methodology combines per-layer search of fixed and dynamic codebook pairs selected by a per-block selection bit, signed per-block scales, activation-weighted cosine selection, and multiple-choice knapsack promotion of sensitive layers with outlier and sparse-residual correction. Fixed codebooks include NF4, BOF4, Split87, and SH4; per-layer optimized codebooks (DD4) are hosted in LUT SRAM. A new hardware-efficient LUT output format (HIF) is proposed to improve performance, energy, and cost. Across six open model families, the recommended FP6 operating point (E2M3sUE4M4, 6.5 bpw) achieves lower weight reconstruction error than the conventional per-layer-POT FP8 baseline (E4M3, 8.0 bpw) at 1.5 bpw lower storage cost, demonstrating that block-scaled small atoms with carefully chosen scale precision can replace conventionally-deployed FP8. Full evaluation across the 4.5--6 bpw range, including layer promotion and sparse residual correction, is reported in a companion paper.

Earl Killian

Mixed-Precision Quantization LLM Quantization Weight-Only Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

May 13, 2026cs.LG

High-Rate Quantized Matrix Multiplication II

This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix

Σ_X

of the columns of the second factor is available. This setting arises in the ubiquitous task of weight-only post-training quantization of LLMs. Weight-only quantization is related to the problem of weighted mean squared error (WMSE) source coding, whose classical (reverse) waterfilling solution dictates how one should distribute rate between coordinates of the vector. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally. A recent scheme (known as ``WaterSIC'') that only uses scalar INT quantizers is analyzed and its high-rate performance is shown to be (a) basis free (i.e., characterized by the determinant of

Σ_X

and, thus, unlike existing schemes, is immune to applying random rotations); and (b) within a multiplicative factor of

\frac{2πe}{12}

(or 0.25 bit/entry) of the information-theoretic distortion limit. GPTQ's performance, in turn, is affected by the choice of basis, but for a random rotation and actual

Σ_X

from Llama-3-8B we find it to be within 0.1 bit (depending on the layer type) of WaterSIC, suggesting that GPTQ with random rotation is also near optimal, at least in the high-rate regime.

Or Ordentlich, Yury Polyanskiy

the Hebrew University of Jerusalem, Israel · MIT, USA

LLM Quantization Rate-Distortion Theory Rate-Distortion Optimization Weight-Only Quantization Post-Training Quantization Neural Network Quantization

May 9, 2026cs.LG

LAQuant: A Simple Overhead-free Large Reasoning Model Quantization by Layer-wise Lookahead Loss

Large reasoning models (LRMs) reach competition-level math and coding accuracy via long autoregressive decoding, making per-token decoding cost a primary deployment concern. Weight quantization is the standard tool for acceleration, but representative recipes -- including state-of-the-art end-to-end (E2E) QAT -- lose accuracy on long-decoding reasoning benchmarks despite preserving perplexity and short-decode accuracy. Through a systematic gradient-direction analysis, we identify two factors driving this gap: (i) KV-cache fidelity preservation under the QAT loss, which E2E supervision attenuates via the softmax Fisher metric; and (ii) Hessian-subspace alignment between calibration data and the deployment distribution. We propose LookAhead Quantization (LAQuant), a layer-wise weight-only QAT method that addresses both factors without online-transform overhead by combining reasoning-domain calibration with a one-layer lookahead loss whose implicit cross-layer co-adaptation preserves the next-layer residual stream. For Qwen3-4B under W3G128 quantization, LAQuant improves AIME25 Pass@1 over ParoQuant by 15.11pp (1.93pp over ParoQuant++ at matched calibration) while achieving a 3.42x decoding speedup over FP16 on RTX A6000, compared with ParoQuant's 3.01x.

Euntae Choi, Sumin Song, Sungjoo Yoo

Seoul National University

LLM Quantization Quantization-Aware Training LLM Inference Acceleration Weight-Only Quantization Neural Network Quantization

May 9, 2026cs.LG

AAAC: Activation-Aware Adaptive Codebooks for 4-bit LLM Weight Quantization

Post-training weight-only quantization to 4 bits is widely used to reduce the memory and compute costs of large language model inference. Existing PTQ methods, such as AWQ and GPTQ, improve how weights are mapped onto a fixed 4-bit grid through scaling, clipping, or error compensation. To further improve accuracy, methods such as OmniQuant and QuIP# uses gradient-assisted algorithms at the cost of hours of quantization time. In this work, we propose AAAC (Activation-Aware Adaptive Codebooks), a lightweight method for 4-bit LLM weight quantization. AAAC replaces the fixed scalar codebook used in standard quantization with two small learned scalar codebooks (64 bytes) per layer. Each group of weights selects the codebook that minimizes activation-weighted reconstruction error, encoding the choice in the unused sign bit of the group's positive scale and adding zero storage overhead. AAAC completes in 3--30 minutes on a single GPU, and adds no memory beyond the model itself. We evaluate against AWQ, GPTQ, IF4, GPTVQ, OmniQuant, SqueezeLLM, and QuIP# across model families. AAAC outperforms baselines at orders-of-magnitude less quantization time.

Beshr IslamBouli, David Jin

Massachusetts Institute of Technology, Cambridge, MA, USA.

LLM Quantization 4-Bit Quantization Weight-Only Quantization Post-Training Quantization Neural Network Quantization

May 6, 2026cs.LG

OSAQ: Outlier Self-Absorption for Accurate Low-bit LLM Quantization

Large Language Models (LLMs) have demonstrated remarkable capabilities. However, their massive parameter scale leads to significant resource consumption and latency during inference. Post-training weight-only quantization offers a promising solution by reducing model size and accelerating token generation through alleviating the memory-bound issue. Nevertheless, the presence of inherent systematic outliers in weights continues to be a major obstacle. While existing methods, such as scaling and rotation, attempt to address this issue, the performance remains unsatisfactory. In this paper, we propose Outlier Self-Absorption Quantization (OSAQ), which performs additive weight suppression guided by the second-order low-rank property for low-bit weight-only quantization of LLMs. Specifically, we observe that the Hessian exhibits low-rank consistency across different inputs, with certain directions consistently showing vanishing curvature. Leveraging this property, we identify a stable null space of the Hessian and then construct an additive weight transformation by linearly combining the vectors within this null space, thereby suppressing weight outliers without affecting the task loss. This additive transformation can be absorbed into the weights offline, requiring no inter-layer transformations and introducing no inference overhead. Moreover, the construction is efficiently achieved by a closed-form solution, without resource-intensive training or iterative procedures. Extensive experiments demonstrate that OSAQ effectively suppresses outliers and enhances low-bit quantization performance. For instance, in 2-bit quantization, OSAQ, when integrated with GPTQ, achieves over 40% lower perplexity compared to vanilla GPTQ.

Zhikai Li, Zhen Dong, Xuewen Liu +2

Institute of Automation, Chinese Academy of Sciences · University of California, Santa Barbara.

LLM Quantization Weight-Only Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Nov 9, 2025cs.CL

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 \href{https://anonymous.4open.science/r/TAQ-9217/README.md}{\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

Mixed-Precision Quantization LLM Quantization Weight-Only Quantization Post-Training Quantization Neural Network Quantization

Jul 24, 2025cs.LG

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 Quantization LLM Quantization Weight-Only Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Date pendingcs.CL

LC-QAT: Data-Efficient 2-Bit QAT for LLMs via Linear-Constrained Vector Quantization

Quantization-aware training (QAT) is essential for extremely low-bit large language models (LLMs). Current QAT methods are mainly based on scalar quantization (SQ), which enables efficient optimization but suffers from severe performance degradation at 2-bit precision. On the other hand, vector quantization (VQ) provides substantially higher representational capacity, but its discrete codebook lookup prevents end-to-end training. We propose LC-QAT, a 2-bit weight-only VQ-QAT framework that represents quantized weights via a learned affine mapping over discrete vectors, which yields a high-quality PTQ initialization and enables fully differentiable end-to-end optimization without explicit codebook lookup in the training forward pass. This strong post-training initialization makes LC-QAT highly data-efficient. Experiments across diverse LLMs demonstrate that LC-QAT consistently outperforms state-of-the-art QAT methods while using only 0.1%--10% of the training data. Our results establish LC-QAT as a practical and scalable solution for extreme low-bit model deployment. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.

Haoyu Wang, Xingyu Yu, Haiyan Zhao +2

Department of Computer Science and Technology, Tsinghua University, Beijing, China · School of Software and Microelectronics, Peking University, Beijing, China · College of Computer Science and Technology, National University of Defense Technology, Hunan, China.

LLM Quantization Quantization-Aware Training Vector Quantization Weight-Only Quantization Neural Network Quantization Data-Efficient Learning