Neural Network Quantization

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36 papers in the last four weeks, up 125% on the four weeks before. 0.4% of all new papers.

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Latest papers 270

May 19, 2026cs.LG

Block-Sphere Vector Quantization

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: EDEN and TurboQuant are favorable for MSE distortion, EDEN is also effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison further clarifies that EDEN provides particularly strong guarantees for expected distortion measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.

Heesang Ann, Joongkyu Lee, Min-hwan Oh

Seoul National University

Rotation-Based Quantization Vector Quantization Neural Network Quantization

May 19, 2026cs.LG

OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond

The rapid advancement toward long-context reasoning and multi-modal intelligence has made the memory footprint of the Key-Value (KV) cache a dominant memory bottleneck for efficient deployment. While the established per-channel quantization effectively accommodates intrinsic channel-wise outliers in Key tensors, its efficacy diminishes under extreme compression. In this work, we revisit the inherent limitations of the per-channel quantization paradigm from both empirical and theoretical perspectives. Our analysis identifies Token Norm Imbalance (TNI) as the primary bottleneck to quantization fidelity. We demonstrate that TNI systematically amplifies errors when shared quantization parameters are required to span token groups exhibiting substantial norm disparities. Instead of relying on intricate quantization pipelines (e.g., TurboQuant), we propose OScaR (Omni-Scaled Canalized Rotation), an accurate and lightweight KV cache compression framework for X-LLMs (i.e., text-only, multi-modal, and omni-modal LLMs). Advancing the per-channel paradigm, OScaR employs Canalized Rotation followed by Omni-Token Scaling to mitigate TNI-induced sequence-dimensional variance both effectively and efficiently, further supported by our optimized system design and CUDA kernels. Extensive evaluations across X-LLMs show that OScaR consistently outperforms existing methods and achieves near-lossless performance under INT2 quantization, establishing it as a robust, low-complexity, and universal framework that defines a new Pareto front. Compared with the BF16 FlashDecoding-v2 baseline, our OScaR implementation achieves a notable up to 3.0x speedup in decoding, reduces memory footprint by 5.3x, and increases throughput by 4.1x. The code for OScaR is publicly available at https://github.com/ZunhaiSu/OScaR-KV-Quant.

Zunhai Su, Rui Yang, Chao Zhang +11

Tsinghua University · Meituan LongCat Team · The University of Hong Kong +3

KV Caching Rotation-Based Quantization Memory-Efficient Inference LLM Inference Acceleration KV-Cache Quantization Low-Bit Quantization+1

May 19, 2026cs.LG

Quant.npu: Enabling Efficient Mobile NPU Inference for on-device LLMs via Fully Static Quantization

Large language models (LLMs) are increasingly deployed on mobile devices, where Neural Processing Units (NPUs) necessitate fully static quantization for optimal inference efficiency. However, existing post-training quantization (PTQ) methods predominantly rely on dynamic activation quantization, rendering them incompatible with NPU hardware constraints. To bridge the gap between high-fidelity PTQ and NPU-constrained inference, we propose Quant.npu, a integer-only fully static quantization framework. It incorporates learnable quantization parameters and rotation matrices, enabling low-bit activation-weight quantization without runtime quantization parameters re-computation. Crucially, we identify that initialization and selective optimization of quantization parameters is pivotal for optimization stability, as improper initialization and naive joint optimization induce gradient instability that disrupts the optimization of rotation matrices. To address this, we propose a rotation-and-bit-width-aware initialization tailored to diverse activation profiles and a distribution-aware selective optimization (two-stage quantization pipeline) tailored to rotated and unrotated tensors. Furthermore, we introduce a sensitivity-guided adaptive mixed-precision scheme to balance accuracy with inference efficiency. Extensive experiments on real-world mobile NPUs demonstrate that Quant.npu achieves comparable accuracy to state-of-the-art methods, while reducing inference latency by up to 15.1%.

Jinghe Zhang, Daliang Xu, Chenghua Wang +5

Mixed-Precision Quantization LLM Quantization AI Accelerator Inference On-Device Language Model Inference Post-Training Quantization Neural Network Quantization

May 19, 2026cs.LG

TORQ: Two-Level Orthogonal Rotation for MXFP4 Quantization

As Large Language Models (LLMs) advance toward practical deployment, the Microscaling FP4 (MXFP4) format has emerged as a cornerstone for next-generation low-bit inference, owing to its ability to balance high dynamic range with hardware efficiency. However, directly applying MXFP4 to LLM activation quantization inevitably leads to significant accuracy degradation. In this paper, we theoretically analyze the error structure of MXFP4 activation quantization, revealing that the root cause of this performance drop lies in two structural imbalances between activation distributions and the MXFP4 block floating-point format: (1) extreme inter-block variance imbalance and (2) intra-block codebook utilization imbalance. To address these challenges, we propose TORQ (Two-level Orthogonal Rotation for MXFP4 Quantization), a training-free Post-Training Quantization (PTQ) framework designed to reshape the geometric properties of the activation space through optimal coordinate transformations. At the macroscopic level, TORQ leverages the Schur-Horn theorem to redistribute activation energy via inter-block orthogonal rotation, preventing high-variance blocks from driving up shared scaling factors and thereby preserving the precision of small-magnitude elements. At the microscopic level, TORQ employs maximum-entropy-guided intra-block rotation to alleviate codebook collapse and maximize the MXFP4 codebook's information capacity. Experiments on mainstream LLMs such as LLaMA3 and Qwen3 show that TORQ significantly improves the accuracy of MXFP4 activation quantization compared to existing methods: on Qwen3-32B, the perplexity on WikiText is reduced to 8.43 (vs. 7.61 for BF16), and the average accuracy increases from 38.40% with direct RTN to 73.63% (vs. 74.82% for BF16), substantially narrowing the gap between 4-bit floating-point quantization and full-precision inference.

Zukang Xu, Xing Hu, Dawei Yang

1Houmo AI.

LLM Quantization Rotation-Based Quantization Activation Quantization Post-Training Quantization Neural Network Quantization

May 18, 2026cs.LG

A Geometric Analysis of Sign-Magnitude Asymmetry in a ReLU + RMSNorm Block under Ternary Quantization

Pre-norm Transformers with RMSNorm tolerate ternary {-1,0,+1} weight quantization with surprisingly small loss (Ma et al., 2024). We give a geometric explanation via sign-magnitude decomposition of weight perturbations. In a two-layer ReLU + RMSNorm model with i.i.d. Gaussian weights, sign-flips produce

π/(π-2) \approx 2.75

times more transverse output energy than sign-preserving magnitude perturbations of equal Frobenius norm, as the flip rate

p \to 0

(Theorem 3). The mechanism: ReLU creates a hidden-space directional asymmetry between the two perturbation types, which RMSNorm's transverse-projection Fréchet derivative selectively exposes. Sign-quantization error is itself a sign-preserving perturbation with angular alignment

\cos^2 \to 2/π

(Theorem 4); its post-ReLU radial fraction (

0.365

) matches the pre-ReLU value

1-2/π

within

0.4\%

, so ReLU is approximately transparent to ternary error. Multi-layer compounding of the

2.75\times

factor is not experimentally supported; the gap to real-model sign sensitivity arises from outlier features violating delocalization. For an input dimension with amplitude

α

, a single sign-flip produces post-ReLU energy amplified by

R \approx nα^2

relative to a delocalized entry. On TinyLlama-1.1B, at linear response (

p \leq 0.5\%

), count-matched NLL leverage stabilizes at

\sim 10\times \approx n\mathbb{E}[α^2]

, matching the per-entry theory; the all-column NLL ratio of

5.0\times

falls within

R_{\mathrm{col}} \leq 19

(

67\times

PPL gap reflects metric nonlinearity). Measured outlier

α

at layer 12 (median

0.024

, max

0.26

) confirms heavy-tailed concentration. The Bussgang constant

2/π

, RMSNorm geometry, and ReLU half-space structure together explain sign-magnitude asymmetry in pre-norm models, with

R \propto nα^2

accounting for real-model deviations.

Lei Dong

Independent Researcher

LLM Quantization Ternary Quantization Neural Representation Geometry Neural Network Quantization

May 18, 2026cs.LG

MARR: Module-Adaptive Residual Reconstruction for Low-Bit Post-Training Quantization

Recently, residual reconstruction-based model quantization methods have achieved promising performance in low-bit post-training quantization (PTQ) by introducing cross-layer residuals to reduce error accumulated from previous layers.However, these residuals may also introduce additional bias arising from the Hessian-approximation (HA) assumption underlying reconstruction-based PTQ, leading to suboptimal quantization performance.In this work, we analyze that multiplying the residual term by a scaling coefficient provides a direct way to mitigate the HA bias associated with residual strength, while preserving accumulated-error correction. More importantly, we observe that this trade-off is module-dependent, making a single global residual strength insufficient to balance effective correction and residual-related bias across modules.Based on these observations, we propose Module-Adaptive Residual Reconstruction (MARR), which assigns a module-specific scaling coefficient to adaptively balance accumulated-error correction and residual-related HA bias for each module.To avoid expensive per-module coefficient search and obtain a stable coefficient estimate, we design a Proportional-Integral-Derivative (PID)-based adaptive update strategy that uses reconstruction error as feedback to progressively refine this coefficient. Experiments on several typical large language models (LLMs) and vision transformers (ViTs) demonstrate the effectiveness of MARR under low-bit quantization (less than or equal to 4-bit), achieving up to 20.2% performance gains on LLMs and up to 4.6% relative gains on ViTs over the residual reconstruction state-of-the-art methods.Code will be made publicly available upon acceptance.

Le Su, Xing Luo, Zhi Jin

School of Intelligent Systems Engineering Shenzhen Campus of Sun Yat-sen University Shenzhen, Guangdong 518107, China · Department of Frontier Research Peng Cheng Laboratory Shenzhen, Guangdong 518055, China

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

May 18, 2026cs.LG

Attention Sinks and Outliers in Attention Residuals

We propose OASIS, an outlier- and sink-aware technique built on inter-layer null signaling. As AttnResidual architectures introduce an additional depth-wise normalization channel, they improve inter-layer routing flexibility but also exacerbate attention sinks, activation outliers, and the resulting degradation in inference stability and quantization robustness. OASIS addresses this issue by introducing a Softmax1-based null space and coupling token-level null evidence to depth routing through an inter-layer null signal, thereby reducing sink-dominated routing and improving structural robustness. Theoretically, we show that the dual-normalization design of AttnResidual intensifies sink formation and quantization brittleness. Experimentally, we compare OASIS against five baselines on three real-world datasets and observe consistent improvements in both attention sink and post-quantization performance. Notably, OASIS achieves an average reduction of 9.26% in maximum infinity norm and 2.60% in average kurtosis across the evaluated settings, while lowering perplexity by 75.85% under W8A8 and improving GSM8K Pass@1 by 12.42% under W4A4.

Haozheng Luo, Haoran Dai, Shaoyang Zhang +10

Department of Computer Science, Northwestern University · Department of Computer Science, Illinois Institute of Technolog · Department of Computer Science and Engineering, University of Michigan +5

LLM Quantization Attention Residual Connections Activation Outliers Attention Sinks Neural Network Quantization

May 18, 2026cs.LG

OSCAR: Offline Spectral Covariance-Aware Rotation for 2-bit KV Cache Quantization

INT2 KV-cache quantization is attractive for long-context LLM serving, but it remains difficult to make both accurate and deployable. Simple rotations such as Hadamard transforms reduce outliers, but still degrade at INT2 because they are not aligned with downstream attention. We propose OSCAR, an Ultra-low-bit KV Cache quantization method that estimates attention-aware covariance structures offline and uses them to derive fixed rotations and clipping thresholds for quantization. In this way, it aligns KV quantization with the covariance structures that attention actually consumes. More importantly, we not only provide theoretical justification but also develop a fully deployable OSCAR system with a custom INT2 attention kernel that remains compatible with paged KV-cache serving and fused kernel pipelines, enabling seamless integration into modern LLM serving frameworks such as SGLang and vLLM. We evaluate our methods on recent reasoning models with reasoning traces of up to 32k tokens across 5 tasks. On Qwen3-4B-Thinking-2507 and Qwen3-8B, OSCAR reduces the BF16 accuracy gap to 3.78 and 1.42 points, respectively, while naive rotation INT2 collapses to nearly zero. We further scale OSCAR to Qwen3-32B and GLM-4.7 (358B params), where it remains effectively on par with BF16. On long context - RULER-NIAH up to 128K, OSCAR remains robust on both Qwen3 models, while naive rotation INT2 collapses. System-wise, OSCAR reduces KV-cache memory by approximately 8x, improves throughput by up to 7x at large batch sizes under the same memory budget, and accelerates batch-size-1 decoding by up to 3x over BF16 due to reduced memory bandwidth overhead.

Zhongzhu Zhou, Donglin Zhuang, Jisen Li +4

Together AI · University of Sydney · University of Illinois Urbana-Champaign

Rotation-Based Quantization LLM Inference Acceleration KV-Cache Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

May 18, 2026stat.ML

StatQAT: Statistical Quantizer Optimization for Deep Networks

Quantization is essential for reducing the computational cost and memory usage of deep neural networks, enabling efficient inference on low-precision hardware. Despite the growing adoption of uniform and floating-point quantization schemes, selecting optimal quantization parameters remains a key challenge, particularly for diverse data distributions encountered during training and inference. This work presents a novel statistical error analysis framework for uniform and floating-point quantization, providing theoretical insight into error behavior across quantization configurations. Building on this analysis, we propose iterative quantizers designed for arbitrary data distributions and analytic quantizers tailored for Gaussian-like weight distributions. These methods enable efficient, low-error quantization suitable for both activations and weights. We incorporate our quantizers into quantization-aware training and evaluate them across integer and floating-point formats. Experiments demonstrate improved accuracy and stability, highlighting the effectiveness of our approach for training low-precision neural networks.

Mehmet Aktukmak, Daniel Huang, Ke Ding

Intel

Quantization-Aware Training Activation Quantization Neural Network Quantization

May 17, 2026cs.LG

Q-LocalAdam: Memory-Efficient Client-Side Adaptive Optimization for Edge Federated Learning

Federated learning on edge devices must cope with non-IID client data and tight memory budgets. Adaptive optimizers like Adam stabilize training under data heterogeneity but require storing full-precision momentum and variance states, often tripling client memory overhead. This limits deployable model sizes and concurrent federated jobs on resource-constrained devices. We empirically observe that momentum and variance in federated Adam exhibit fundamentally different statistical properties: momentum values are symmetric and bounded, while variance spans eight orders of magnitude with log-normal structure. Motivated by this asymmetry, we propose \textbf{Q-LocalAdam}, which applies distribution-aware 8-bit quantization block-wise linear encoding for momentum and log-space encoding for variance while keeping model parameters in full precision. Across CIFAR-10 and CIFAR-100 under varying data heterogeneity (

α\in \{0.1, 0.5, 1.0, \text{IID}\}

), Q-LocalAdam achieves

3.37\times

optimizer memory reduction with no accuracy loss under moderate heterogeneity and significant improvements under extreme heterogeneity (e.g., +5.74pp on CIFAR-100,

α=0.1

). Multi-seed validation confirms statistical significance (

p<0.01

). In contrast, naive uniform quantization degrades to random performance, demonstrating that distribution-aware design is essential. Q-LocalAdam enables larger models and more concurrent workloads on memory-constrained edge devices without modifying the federated protocol.

Vedant Waykole, Haroon R. Lone

IISER Bhopal · India

Non-IID Federated Learning Edge ML Neural Network Quantization Federated Learning

May 17, 2026cs.LG

Covariance Structure and Coordinate Heterogeneity Govern Binary Quantization of Contrastive Embeddings

Binary quantization (BQ) compresses high-dimensional embeddings into one or two bits per coordinate, enabling nearest neighbor search at extreme speed. Yet a striking puzzle persists: BQ achieves competitive recall on contrastive embeddings but fails on others -- and two leading systems adopt diametrically opposite strategies (random rotation vs. preserving coordinate axes) without a common theory explaining when each is appropriate. We address this puzzle by connecting the Gaussian structure recently established for InfoNCE-trained representations to a statistical framework for BQ quality. Our analysis reveals two distinct roles of the covariance matrix. First, the full covariance structure -- not merely its diagonal -- determines the absolute level of ranking fidelity, with off-diagonal correlations contributing 30--50% of the signal. Second, coordinate heterogeneity (the non-uniformity of per-coordinate variances) governs key design choices: how much each additional bit contributes, and whether random rotation helps or hurts. We derive approximate expressions for ranking fidelity under a Gaussian model, show that the magnitude bit carries information proportional to heterogeneity, and show that random rotation destroys precisely the signal that one paradigm exploits while creating the isotropy that the other requires. A phenomenological scaling law predicts fidelity across models and dimensions. Experiments on 18 datasets spanning 9 embedding families support the main predictions and provide, to our knowledge, the first principled design guide for binary quantization systems.

Wenxuan Xiao

Changsha University

Neural Representation Geometry Embedding Compression Low-Bit Quantization Neural Network Quantization

May 16, 2026cs.CV

CAR-SAM: Cross-Attention Reconstruction for Post-Training Quantization of the Segment Anything Model

Segment Anything Models (SAMs) are extensively used in computer vision for universal image segmentation, but deploying them on resource-constrained devices is challenging due to their high computational and memory demands. Post-Training Quantization (PTQ) is a widely used technique for model compression and acceleration. However, existing PTQ methods fail to consider the cross-attention architecture in the SAM decoder. This degradation primarily stems from the unique challenges posed by SAMs: (1) Attention dissipation, where the attention information in the decoder, which is crucial for representing segmentation masks, collapses into a diffuse and non-semantic form under low-bit quantization; and (2) Reconstruction oscillation, where bidirectional coupling within the two-way transformer introduces cross-branch error interference and destabilizes convergence. To tackle these issues, we propose CAR-SAM, a unified quantization framework tailored for SAMs. Firstly, to mitigate attention dissipation, we introduce MatMul-Aware Compensation (MAC) mechanism that transfers activation-induced quantization errors from MatMul to preceding linear weights. Secondly, to mitigate oscillation in decoder optimization, we develop a Joint Cross-Attention Reconstruction (JCAR) strategy that jointly reconstructs coupled attention branches, suppressing oscillatory behavior and promoting stable convergence. Extensive experiments show that CAR-SAM robustly quantizes SAM models down to 4-bit precision, surpassing existing methods by 14.6% and 6.6% mAP on SAM-B and SAM-L respectively.

Houji Wen, Jiangyong Yu, Jun Li +1

1Nanjing University of Science and Technology · 2Houmo AI

Cross-Attention 4-Bit Quantization Post-Training Quantization Neural Network Quantization

May 16, 2026cs.CL

E-PMQ: Expert-Guided Post-Merge Quantization with Merged-Weight Anchoring

Low-resource deployment constraints have made model quantization essential for deploying neural networks while preserving performance. Meanwhile, model merging has become an increasingly practical low-resource strategy for integrating multiple task- or domain-specialized experts into a single model without joint training or multi-model serving. Together, quantization and model merging enable an efficient low-resource deployment pipeline by integrating multiple experts into one low-bit model. We formulate this setting as Post-Merge Quantization (PMQ). We show that directly applying post-training quantization (PTQ) to a merged model is unreliable because two distinct deviations are coupled: the quantization deviation introduced by low-bit reconstruction and the expert-relative merging deviation inherited from model merging. To mitigate these deviations, we propose E-PMQ, an expert-guided PMQ framework that uses source expert weights to provide expert- guided output targets during layer-wise calibration, together with merged-weight anchoring to stabilize the calibration and preserve the integrated behavior of the merged model. On CLIP-ViT-B/32 eight-task merging, E-PMQ improves 4-bit GPTQ from 65.0% to 73.6% under Task Arithmetic and from 69.1% to 74.8% under TIES-Merging. On harder settings, E-PMQ improves GPTQ from 34.8% to 76.7% on 20-task CLIP-ViT-L/14 and from 78.26% to 83.34% on FLAN-T5- base GLUE. These results demonstrate that E-PMQ enables effective post-merge quantization and low-bit deployment.

Wenjun Wang, Yanggan Gu, Shuo Cai +4

The Hong Kong Polytechnic University · PolyU-Daya Bay Technology and Innovation Research Institute

4-Bit Quantization Post-Training Quantization Neural Network Quantization

May 16, 2026cs.CV

DiRotQ: Rotation-Aware Quantization for 4-bit Diffusion Transformers

Diffusion Transformers (DiTs) achieve state-of-the-art image generation quality but incur substantial memory and computational costs at inference. While aggressive Post-Training Quantization (PTQ) to 4-bit precision offers significant efficiency gains, it typically results in severe quality degradation. Existing approaches, including smoothing-based methods, mixed-precision schemes, rotation techniques, and low-rank residual methods, partially mitigate this issue but still leave a noticeable gap to FP16/BF16 performance. In this work, we introduce DiRotQ, a W4A4 PTQ framework that mitigates this degradation through rotation-aware activation quantization. DiRotQ identifies a low-rank subspace capturing dominant activation variance via Principal Component Analysis (PCA), preserving coefficients in this subspace at higher precision while quantizing the remaining components to 4-bit. Activations are rotated into the PCA basis at inference time using calibration-derived orthogonal transformations, while the inverse rotation is fused into the layer weights offline. Combined with GPTQ-based weight quantization, DiRotQ achieves an FID (lower is better) of 15.9 and PSNR (higher is better) of 19.1 dB on PixArt-Σ over the MJHQ-30K dataset, outperforming the prior state-of-the-art SVDQuant (FID 18.9, PSNR 17.6) under the same INT W4A4 setting. Beyond standard metrics, we introduce a VLM-as-a-Judge evaluation protocol for diffusion model quantization, the first such evaluation in this setting, providing a more holistic assessment of perceptual quality and prompt alignment under aggressive compression. On the systems side, we implement a Triton-based custom kernel to enable efficient end-to-end inference, reducing memory usage of the 12B FLUX.1-dev model by 2.1x and delivering 2.3x speedup over the BF16 baseline, on a 24 GB RTX 4090 GPU.

Sayeh Sharify, Mahsa Salmani, Hesham Mostafa

d-Matrix Santa Clara, CA 95054

Diffusion Transformer Diffusion Model Quantization 4-Bit Quantization Rotation-Based Quantization Activation Quantization Post-Training Quantization+2

May 15, 2026cs.CV

Not All Tasks Quantize Equally: Fisher-Guided Quantization for Visual Geometry Transformer

Feed-forward 3D reconstruction models, represented by Visual Geometry Grounded Transformer (VGGT), jointly predict multiple visual geometry tasks such as depth estimation, camera pose prediction, and point cloud reconstruction in a single forward pass. They have been widely adopted in 3D vision applications, but their billion-scale parameters bring substantial memory and computation overhead, posing challenges for on-device deployment. Post-Training Quantization (PTQ) is an effective technique to reduce this overhead. Existing PTQ methods for feed-forward 3D models mainly focus on handling heavy-tailed activation distributions and constructing diverse calibration datasets. However, we observe that feed-forward 3D models predict multiple geometric attributes through a shared backbone, where different transformer blocks and hidden channels contribute distinctly to each task, resulting in substantially different sensitivities to quantization errors across tasks, blocks, and channels. Consequently, treating all tasks equally over-emphasizes insensitive tasks and causes significant accuracy loss on the sensitive ones. To address this issue, we propose Fisher-Guided Quantization (FGQ) for feed-forward 3D reconstruction models. Specifically, FGQ uses the diagonal Fisher information matrix to quantify the different sensitivities across tasks, blocks, and channels, and incorporates these sensitivities into the Learnable Affine Transformation during calibration to better preserve the channels and blocks most critical to each task. Extensive experiments across camera pose estimation, point map reconstruction, and depth estimation show that FGQ consistently outperforms state-of-the-art quantization baselines on VGGT, achieving up to 39% relative improvement under the 4-bit quantization. Code is available at https://github.com/ypzhng/FGQ.

Yipu Zhang, Jintao Cheng, Weilun Feng +5

Department of Electronic and Computer Engineering, HKUST · State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences +2

Feed-Forward 3D Reconstruction Post-Training Quantization Neural Network Quantization

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 14, 2026cs.CV

Nonlinear Bipolar Compensation: Handling Outliers in Post-Training Quantization

Network quantization has emerged as one of the most practical model compression techniques, which significantly reduces a model's memory and compute consumption by mapping floating-point numbers to low-bit representations. However, existing quantization methods typically suffer from the speed-accuracy tradeoff and limited generalization. To address these issues, recent compensation-based methods offer an efficient yet general solution by introducing additional lightweight linear layers into the quantized network. However, the accuracy of these methods suffers from their limited compensation capability and high sensitivity to outliers. In this paper, we propose Nonlinear Bipolar Compensation (NBC), a post-training quantization approach that introduces nonlinear compensation to reduce the effect of outliers. We further design Bipolar Logarithmic Transformation (BLT), which compresses outliers by mapping both the quantized input and the quantization error into a transformed space. A simple linear layer is then applied for compensation in the transformed space, preserving the efficiency of our method. Extensive experiments across various tasks, models, and quantization methods confirm the effectiveness, efficiency, robustness, and generality of our NBC approach.

Peilin Sun, Jianxin Wu

State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China

Activation Outliers Post-Training Quantization Neural Network Quantization

May 14, 2026cs.LG

XFP: Quality-Targeted Adaptive Codebook Quantization with Sparse Outlier Separation for LLM Inference

We introduce XFP, a dynamic weight quantizer for LLM inference that inverts the conventional workflow: the operator specifies reconstruction quality floors on per-channel cosine similarity (one strict floor for attention and shared experts, one lazy floor for routed-expert MoE); XFP determines codebook size, outlier budget, and packing per layer automatically -- no Hessian, no calibration data, no manual bit-width selection. Each weight matrix is decomposed into a sparse fp16 outlier residual and a dense sub-byte index tensor into a per-group learned codebook. Two storage modes share one auto-select frontend and one fused decode kernel: V2 (per-channel Lloyd) and V2a (shared library of L=32 codebooks per layer). On Qwen3.5-122B-A10B under V2, XFP reaches 138 tok/s single-stream decode on workstation hardware (RTX PRO 6000 Blackwell, TP=2) at 94.49% GSM8K strict-match (3 seeds, n=3957), and is 49% faster than Marlin INT4 at TP=1. For models that do not fit in the target memory envelope, we present the H-Process: a quality-driven iteration over the two cosine thresholds that finds the operating point at which the model just fits while still producing sensible output. Three constraints define its search space: the operator-set thresholds, an OOM boundary at quantize-on-load, and a garbage boundary in generation (cosine similarity steers; benches verify). On Qwen3.5-397B-A17B (512 routed experts/layer), the H-Process fits the full expert population into 2x96 GB at ~3.4 effective bits and delivers 100.9 tok/s long-output decode at 66.72% GSM8K strict-match on the full 1319-problem set (single seed at submission; multi-seed evaluation in progress), exceeding INT4 with routed-expert pruning on memory, throughput, and accuracy simultaneously.

Thomas Witt

Gemini Stiftung Leipzig

LLM Quantization Vector Quantization LLM Inference Acceleration Post-Training Quantization Neural Network Quantization

May 13, 2026cs.LG

Provable Quantization with Randomized Hadamard Transform

Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random rotations yield clean theoretical guarantees, they require

Θ(d^2)

time. The randomized Hadamard transform

HD

reduces this cost to

O(d \log d)

, but its discrete structure complicates analysis and leads to weaker or purely empirical compression guarantees. In this work, we study a variant of this approach: dithered quantization with a single randomized Hadamard transform. Specifically, the quantizer applies

HD

to the input vector and subtracts a random scalar offset before quantizing, injecting additional randomness at negligible cost. We prove that this approach is unbiased and provides mean squared error bounds that asymptotically match those achievable with truly random rotation matrices. In particular, we prove that a dithered version of TurboQuant achieves mean squared error

\bigl(π\sqrt{3}/2 + o(1)\bigr) \cdot 4^{-b}

at

b

bits per coordinate, where the

o(1)

term vanishes uniformly over all unit vectors and all dimensions as the number of quantization levels grows.

Ying Feng, Piotr Indyk, Michael Kapralov +2

Vector Quantization Randomized Sketching 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 12, 2026cs.LG

Search Your Block Floating Point Scales!

Quantization has emerged as a standard technique for accelerating inference for generative models by enabling faster low-precision computations and reduced memory transfers. Recently, GPU accelerators have added first-class support for microscaling Block Floating Point (BFP) formats. Standard BFP algorithms use a fixed scale based on the maximum magnitude of the block. We observe that this scale choice can be suboptimal with respect to quantization errors. In this work, we propose ScaleSearch, an alternative strategy for selecting these scale factors: using a fine-grained search leveraging the mantissa bits in microscaling formats to minimize the quantization error for the given distribution. ScaleSearch can be integrated with existing quantization methods such as Post Training Quantization and low-precision attention, and is shown to improve their performance. Additionally, we introduce ScaleSearchAttention, an accelerated NVFP4-based attention algorithm, which uses ScaleSearch and adapted prior techniques to ensure near-0 performance loss for causal language modeling. Experiments show that ScaleSearch reduces quantization error by 27% for NVFP4 and improves language model PTQ by up to 15 points for MATH500 (Qwen3-8B), while ScaleSearchAttention improves Wikitext-2 PPL by upto 0.77 points for Llama 3.1 70B. The proposed methods closely match baseline performance while providing quantization accuracy improvements.

Tanmaey Gupta, Hayden Prairie, Xiaoxia Wu +10

Cornell University, Ithaca, NY, USA · Together AI, USA · University of California San Diego, La Jolla, CA, USA +1

4-Bit Quantization LLM Inference Acceleration Post-Training Quantization Neural Network Quantization

May 12, 2026cs.LG

SOAR: Scale Optimization for Accurate Reconstruction in NVFP4 Quantization

NVFP4 has recently emerged as an efficient 4-bit microscaling format for large language models (LLMs), offering superior numerical fidelity with native hardware support. However, existing methods often yield suboptimal performance due to inflexible scale selection and the coupled treatment of quantization and dequantization scales. To address these issues, we propose Scale Optimization for Accurate Reconstruction (SOAR), a novel post-training quantization framework that improves the accuracy of NVFP4 quantization. At its core, SOAR features Closed-form Joint Scale Optimization (CJSO), which jointly optimizes global and block-wise scales via analytical solutions derived from reconstruction error minimization. Furthermore, it incorporates Decoupled Scale Search (DSS). DSS decouples the high-precision quantization scale from its constrained dequantization counterpart, and performs discrete search to mitigate precision loss from scale quantization. Extensive experiments across multiple LLMs show that our method consistently outperforms existing NVFP4 quantization baselines, achieving superior accuracy under the same memory footprint with no additional hardware overhead. The code and models will be available at https://github.com/steven-bao1/SOAR.

Chengzhu Bao, Xianglong Yan, Zhiteng Li +3

Shanghai Jiao Tong University · Tencent Hunyuan

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

May 12, 2026cs.LG

MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to quantization errors: because the orthogonalization discards the magnitudes of singular values and retains only directional information, even small quantization errors in singular vector directions are amplified in the update. In this work, we propose MuonQ, a low-bit Muon training framework built on the principle of directional fidelity optimization. First, we apply a pre-quantization normalization so that each step introduces quantization errors of the same magnitude, preventing the accumulated error from developing a preferred direction. Second, we introduce a structural decomposition that separately quantizes the dominant singular components via power iteration, ensuring that quantization errors perturb only singular value magnitudes rather than rotating singular vector directions. Third, we adopt

μ

-law companding quantization to allocate higher resolution to densely packed momentum values, shifting the quantization objective from outlier preservation to dense-region distinguishability. Together, these techniques enable stable 4-bit quantization of Muon's optimizer states. Pre-training experiments on GPT-style and LLaMA-style models demonstrate that MuonQ at 4-bit precision closely matches full-precision Muon in both training loss and downstream task accuracy, while reducing optimizer state memory by up to 7.3

\times

. Our code is available at https://github.com/YupengSu/MuonQ.

Yupeng Su, Ruijie Zhang, Ziyue Liu +2

University of California, Santa Barbara

4-Bit Quantization Muon Optimizer Low-Bit Quantization Neural Network Quantization

May 11, 2026cs.LG

ADMM-Q: An Improved Hessian-based Weight Quantizer for Post-Training Quantization of Large Language Models

Quantization is an effective strategy to reduce the storage and computation footprint of large language models (LLMs). Post-training quantization (PTQ) is a leading approach for compressing LLMs. Popular weight quantization procedures, including GPTQ and RTN, suffer in model utility, especially at aggressive quantization levels (sub-4-bit). We propose ADMM-Q, a novel weight quantization algorithm that considers the layer-wise quantization problem. Our algorithm is based on a combinatorial variant of the Alternating Direction Method of Multipliers (ADMM). Our operator-splitting procedure updates weights continuously to minimize the layer-wise reconstruction error, while gradually enforcing the quantization constraints with convergence guarantees. We propose additional algorithmic enhancements (e.g., penalty scheduling, preconditioning, and a local search post-processing step) to make ADMM-Q efficient at LLM scale. ADMM-Q is modular and can be used as a drop-in replacement for any weight quantizer within existing quantization pipelines: ADMM-Q is fully composable with existing techniques including range clipping, learned or random rotations, and activation scaling. Using ADMM-Q in place of GPTQ on Qwen3-8B, we decrease WikiText-2 perplexity in: (i) the W3A16 weight-only setting (12.85

\rightarrow

10.06); (ii) the W4A8 SmoothQuant procedure (9.29

\rightarrow

8.68); and (iii) the W2A4KV4 SpinQuant procedure (66.11

\rightarrow

19.42).

Ryan Lucas, Mehdi Makni, Xiang Meng +2

MIT Operations Research Center · MIT Sloan School of Management · MIT Center for Statistics

LLM Quantization Alternating Direction Method of Multipliers Constrained Optimization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

May 11, 2026cs.LG

LoKA: Low-precision Kernel Applications for Recommendation Models At Scale

Recent GPU generations deliver significantly higher FLOPs using lower-precision arithmetic, such as FP8. While successfully applied to large language models (LLMs), its adoption in large recommendation models (LRMs) has been limited. This is because LRMs are numerically sensitive, dominated by small matrix multiplications (GEMMs) followed by normalization, and trained in communication-intensive environments. Applying FP8 directly to LRMs often degrades model quality and prolongs training time. These challenges are inherent to LRM workloads and cannot be resolved merely by introducing better FP8 kernels. Instead, a system-model co-design approach is needed to successfully integrate FP8. We present LoKA (Low-precision Kernel Applications), a framework that makes FP8 practical for LRMs through three principles: profile under realistic distributions to know where low precision is safe, co-design model components with hardware to expand where it is safe, and orchestrate across kernel libraries to maximize the gains. Concretely, LoKA Probe is a statistically grounded, online benchmarking method that learns activation and weight statistics, and quantifies per-layer errors. This process pinpoints safe and unsafe, fast and slow sites for FP8 adoption. LoKA Mods is a set of reusable model adaptations that improve both numerical stability and execution efficiency with FP8. LoKA Dispatch is a runtime that leverages the statistical insights from LoKA Probe to select the fastest FP8 kernel that satisfies the accuracy requirements.

Liang Luo, Yinbin Ma, Quanyu Zhu +21

Meta AI

Mixed-Precision Quantization GPU Kernel Optimization GPU Acceleration Recommender Systems Neural Network Quantization

May 11, 2026cs.RO

Nano-U: Efficient Terrain Segmentation for Tiny Robot Navigation

Terrain segmentation is a fundamental capability for autonomous mobile robots operating in unstructured outdoor environments. However, state-of-the-art models are incompatible with the memory and compute constraints typical of microcontrollers, limiting scalable deployment in small robotics platforms. To address this gap, we develop a complete framework for robust binary terrain segmentation on a low-cost microcontroller. At the core of our approach we design Nano-U, a highly compact binary segmentation network with a few thousand parameters. To compensate for the network's minimal capacity, we train Nano-U via Quantization-Aware Distillation (QAD), combining knowledge distillation and quantization-aware training. This allows the final quantized model to achieve excellent results on the Botanic Garden dataset and to perform very well on TinyAgri, a custom agricultural field dataset with more challenging scenes. We deploy the quantized Nano-U on a commodity microcontroller by extending MicroFlow, a compiler-based inference engine for TinyML implemented in Rust. By eliminating interpreter overhead and dynamic memory allocation, the quantized model executes on an ESP32-S3 with a minimal memory footprint and low latency. This compiler-based execution demonstrates a viable and energy-efficient solution for perception on low-cost robotic platforms.

Federico Pizzolato, Francesco Pasti, Nicola Bellotto

Dept of Information Engineering, University of Padua, Italy

Robot Navigation Semantic Segmentation Neural Network Quantization

May 10, 2026cs.CV

PermuQuant: Lowering Per-Group Quantization Error by Reordering Channels for Diffusion Models

Large-scale visual generative models have achieved remarkable performance. However, their high computational and memory costs make deployment challenging in resource-constrained scenarios, such as interactive applications and personal single-GPU usage. Post-training quantization (PTQ) offers a practical solution by compressing pretrained models without expensive retraining. However, existing PTQ methods still suffer from severe quality degradation under extremely low-bit settings. In this paper, we identify channel ordering as an important but underexplored factor in per-group quantization. In this setting, each contiguous group shares one quantization scale. When channels with very different statistics are placed in the same group, the scale can be dominated by outliers and cause large quantization errors. Based on this observation, we propose PermuQuant, a simple and effective PTQ framework for low-bit diffusion models. PermuQuant sorts channels by a joint second-moment criterion before per-group quantization, placing channels with similar activation and weight statistics into the same group. It further uses a calibration-based acceptance rule to apply reordering only when the selected permutation reduces quantization error on calibration data. The selected permutations are absorbed into adjacent modules or applied to weights offline, avoiding explicit runtime permutation operations. Extensive experiments on multiple large diffusion models show that PermuQuant consistently reduces quantization error and outperforms existing PTQ baselines. On FLUX.1-dev with an RTX 5090, PermuQuant achieves up to a 1.7

\times

single step speedup and reduces the DiT memory footprint by 3.5

\times

under W4A4 NVFP4 quantization. Code will be available at https://github.com/yscheng04/PermuQuant.

Yongsen Cheng, Kai Liu, Kaiwen Tao +5

Shanghai Jiao Tong University · Huawei Noah’s Ark Lab

Diffusion Model Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization Diffusion Models

May 10, 2026cs.LG

TileQ: Efficient Low-Rank Quantization of Mixture-of-Experts with 2D Tiling

Mixture-of-Experts (MoE) models achieve remarkable performance by sparsely activating specialized experts, yet their massive parameters in experts pose significant challenges for deployment. While low-rank quantization offers a promising route to compress MoE models, existing methods still incur nonnegligible memory overhead and inference latency. To address these limitations, we propose \textsc{TileQ}, a fine-tuning-free post-training quantization (PTQ) method that employs 2D-tiling structured low-rank quantization to share low-rank factors across both input and output dimensions of MoE experts. Furthermore, we introduce an efficient inference technique for \textsc{TileQ} that fuses multiple low-rank expert computations into a single-pass operation, significantly improving hardware utilization. Experiments show that \textsc{TileQ} cuts down additional memory usage up to 10

\times

and reduces inference latency to

\sim

5% while preserving state-of-the-art accuracy.

Hongyaoxing Gu, Xinzhe Chen, Lijuan Hu +1

Institute of Software Chinese Academy of Sciences · University of Chinese Academy of Sciences

Efficient Inference Mixture-of-Experts Inference Mixture-of-Experts Quantization Mixture-of-Experts Models 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