Low-Bit Quantization

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21 papers in the last four weeks, up 62% on the four weeks before. 0.2% of all new papers.

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Latest papers 155

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

Contextual Bandits for Resource-Constrained Devices using Probabilistic Learning

Contextual bandits (CB) are online sequential decision-making problems under partial feedback that underpin many adaptive services. There is a growing demand to deploy CB agents directly on-device, under strict constraints on memory, compute, and energy. However, standard linear CB algorithms are often impractical for resource-constrained devices with their unfavorable scaling in computational and memory costs. Recently, HD-CB, a CB approach based on hyperdimensional computing principles, has been proposed to model and solve CB problems by moving into high-dimensional spaces. HD-CB offers faster convergence, favorable scalability, and improves memory efficiency compared to linear CB algorithms. However, its learning rule is accumulation-based: the values of action vectors grow over time, requiring high precision. While periodic binarization can prevent overflow in low-precision components, it may discard important information about magnitudes and degrade decision quality. This paper introduces probabilistic HD-CB, a low-precision variant that replaces deterministic accumulation with a probabilistic update rule. At each step, only a random subset of vector components is updated, with a time-decaying update probability, and component values are constrained to a predefined range [-k,+k]. This approach enables low-precision components, prevents overflow without periodic binarization, and reduces the expected update cost in proportion to the fraction of updated components. Off-policy evaluation on standardized synthetic CB benchmarks using the Open Bandit Pipeline shows that probabilistic HD-CB consistently outperforms binarized HD-CB at equal precision, while approaching the performance of HD-CB with as few as 3 bits per component.

Marco Angioli, Kevin Johansson, Antonello Rosato +2

Sapienza University of Rome · Orebro University · Linkoping University +1

Hyperdimensional Computing Contextual Bandits Low-Bit Quantization On-Device Inference

May 12, 2026cs.AI

FibQuant: Universal Vector Quantization for Random-Access KV-Cache Compression

Long-context inference is increasingly a memory-traffic problem. The culprit is the key--value (KV) cache: it grows with context length, batch size, layers, and heads, and it is read at every decoding step. Rotation-based scalar codecs meet this systems constraint by storing a norm, applying a shared random rotation, and quantizing one coordinate at a time. They are universal and random-access, but they discard the geometry created by the normalization step. After a Haar rotation, a block of

k

consecutive coordinates is not a product source; it is a spherical-Beta source on the unit ball. We introduce \textsc{FibQuant}, a universal fixed-rate vector quantizer that keeps the same normalize--rotate--store interface while replacing scalar tables by a shared radial--angular codebook matched to this canonical source. The codebook combines Beta-quantile radii, Fibonacci,/,Roberts--Kronecker quasi-uniform directions, and multi-restart Lloyd--Max refinement. We prove that the resulting vector code strictly improves on its scalar product specialization at matched rate, with a high-rate gain that separates into a cell-shaping factor and a density-matching factor. The same construction gives a dense rate axis, including fractional-bit and sub-one-bit operating points, without calibration or variable-length addresses. On GPT-2 small KV caches, \textsc{FibQuant} traces a memory--fidelity frontier from

5\times

compression at

0.99

attention cosine similarity to

34\times

at

0.95

. End-to-end on TinyLlama-1.1B, it is within

0.10

perplexity of fp16 at

4\times

compression and has

3.6\times

lower perplexity than scalar \textsc{TurboQuant} at

b = 2

(

8\times

compression), where scalar random-access quantization begins to fail.

Namyoon Lee, Yongjune Kim

POSTECH

KV Caching Rotation-Based Quantization Vector Quantization KV-Cache Compression KV-Cache Quantization Low-Bit 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

Theory-optimal Quantization Based on Flatness

Post-training quantization has emerged as a widely adopted technique for compressing and accelerating the inference of Large Language Models (LLMs). The primary challenges in LLMs quantization stem from activation outliers, which significantly degrade model performance especially at lower bit precision. While recent approaches attempt to mitigate outliers through linear transformations across feature dimensions, our analysis reveals that the transformed weights and activations still exhibit persistent outlier patterns with concentrated magnitude distributions. In this paper, we first model the mathematical relationship between quantization error and outliers, and then introduce a new metric Flatness to quantify the distribution of outliers. Based on this, we derive the theoretical optimal solution with respect to Flatness. Building on these insights, we propose Bidirectional Diagonal Quantization (BDQ), a novel post-training quantization framework that effectively disperses outlier patterns through optimized matrix transformations. BDQ strategically distributes outlier magnitudes across matrix dimensions via learned diagonal operations. Extensive experiments demonstrate that BDQ establishes a new quantization benchmark. It achieves less than 1% accuracy drop in W4A4 quantization on the LLaMA-3-8B model. In the more challenging W2A4KV16 experiment, compared to state-of-the-art approaches, BDQ reduces the performance gap by 39.1% on the DeepSeek-R1-Distill-LLaMA-70B model.

Xiusheng Huang, Zhe Li, Xuanwu Yin +5

The Key Laboratory of Cognition and Decision Intelligence for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China · School of Artificial Intelligence, University of Chinese Academy of Sciences · Beijing Academy of Artificial Intelligence +2

LLM Quantization Activation Quantization Post-Training Quantization Low-Bit 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 9, 2026cs.CL

Fitting Is Not Enough: Smoothness in Extremely Quantized LLMs

Large language models (LLMs) achieve strong performance but incur high deployment costs, motivating extremely low-bit but lossy quantization. Existing quantization algorithms mainly focus on improving the numerical accuracy of forward computation to eliminate performance degradation. In this paper, we show that extremely quantized LLMs suffer from systematic smoothness degradation beyond numerical precision loss. Through a smoothness proxy, we observe that such degradation becomes increasingly severe as the quantization bit-width decreases. Furthermore, based on sequence neighborhood modeling, we find that quantized models exhibit a rapid reduction of effective token candidates within the prediction neighborhood, which directly leads to a sparser decoding tree and degraded generation quality. To validate it, we introduce a simple smoothness-preserving principle in both post-training quantization and quantization-aware training, and demonstrate that preserving smoothness brings additional gains beyond numerical accuracy. The core goal of this paper is to highlight smoothness preservation as an important design consideration for future extreme quantization methods. Code is available at https://github.com/xuyuzhuang11/FINE.

Yuzhuang Xu, Xu Han, Yuxuan Li +2

1Harbin Institute of Technology, Harbin, China · 2Tsinghua University, Beijing, China

LLM Quantization Post-Training Quantization Low-Bit Quantization

May 8, 2026cs.LG

Finer is Better (with the Right Scaling)

Microscaling is a critical technique for preserving the quality of Large Language Models (LLMs) quantized to ultra-low precision formats. Intuitively, finer block sizes should yield lower quantization error; however, a paradox recently identified by Fasoli et al. (2026) demonstrates that standard abs-max scaling can actually result in degraded model quality as block sizes shrink. In this work, we investigate the underlying mechanics of this phenomenon. We demonstrate that this degradation is not an inherent limitation of finer granularity, but is primarily driven by how elements in smaller blocks statistically cluster closer to their local block maximum, interacting poorly with the coarse subnormal E4M3 values used as scaling factors. Specifically, we show that i) preventing the scaling factor from underflowing to zero mitigates errors caused by extreme underflow, ii) targeted algorithmic interventions like the 4-over-6 methodology that give more flexibility to the choice of scaling factor resolve the paradox for larger values, and iii) a brute-force search establishes an optimal baseline, confirming that the theoretical Mean Squared Error (MSE) strictly improves with finer block sizes. Ultimately, our findings highlight a critical insight for hardware-software co-design: the block-size paradox is partially an artifact of naive scale selection. While using hierarchical scaling factors or wider formats like UE5M3 interchangeably resolves much of the quality loss, we found the 4-over-6 scale selection heuristic can even further improve quality, especially for very small block sizes. Consequently, maximizing the performance of next-generation ML accelerators will require treating silicon format specifications and software scaling algorithms as tightly coupled design choices.

Clemens Schaefer, Gil Tabak

Google LLC, Mountain View, Ca

LLM Quantization 4-Bit Quantization Low-Bit Quantization Neural Network Quantization

May 8, 2026cs.LG

Direction-Preserving Number Representations

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

Bardia Zadeh, George A. Constantinides

Department of Electrical and Electronic Engineering Imperial College London London, United Kingdom

4-Bit Quantization Low-Bit Quantization Neural Network Quantization

May 8, 2026cs.LG

LoopQ: Quantization for Recursive Transformers

Looped language models (LoopLMs) improve parameter efficiency by recursively reusing Transformer blocks, enabling deeper computation under a fixed model size. However, this reuse makes LoopLMs more fragile under post-training quantization (PTQ). We present the first systematic study of quantization in LoopLMs and identify three challenges: distribution shift across roles, state reuse across loop transitions, and recursive error accumulation. To address these challenges, we propose LoopQ, a loop-aware PTQ framework that preserves a shared quantized backbone while introducing lightweight adaptations. LoopQ combines activation scaling, selective transformation, cross-loop state alignment, and trajectory-aware optimization to reduce distributional mismatch within loops and error accumulation across loops. Experiments across seven benchmarks show that, under W4A4 quantization, LoopQ improves average downstream accuracy by 68.8% and reduces average perplexity by 87.7% compared with the strongest static PTQ baseline.

Rui Fang, Hsi-Wen Chen, Ming-Syan Chen

National Taiwan University

Recurrent Transformers Language Modeling Activation Quantization Post-Training Quantization Low-Bit Quantization Recursive Language Models

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

May 4, 2026cs.LG

Statistically-Lossless Quantization of Large Language Models

Model quantization has become essential for efficient large language model deployment, yet existing approaches involve clear trade-offs: methods such as GPTQ and AWQ achieve practical compression but are lossy, while lossless techniques preserve fidelity but typically do not accelerate inference. This paper explores the middle ground of statistically-lossless compression through three complementary notions of losslessness for quantized LLMs. First, task-lossless compression preserves zero-shot benchmark accuracy within natural sampling variance and remains achievable at aggressive bitwidths. Second, we formalize the stricter notion of distribution-lossless compression, requiring the quantized model's next-token distribution to be practically indistinguishable from the original, and propose the Expected Acceptance Rate (EAR), the maximum token-agreement probability under optimal coupling, as a directly interpretable fidelity metric (for example, EAR >= 0.99 indicates 99% agreement). Third, we prove a gamma-squared variance law showing that symmetric quantization inflates noise variance by gamma squared relative to asymmetric quantization, making asymmetry necessary for distribution-lossless fidelity but not for task-level preservation. Using SLQ, a layer-wise non-uniform method with asymmetric quantization and wide bitwidth search, we achieve task-lossless compression at well below 4 bits per parameter (as low as 3.3 bits depending on the model), distribution-lossless compression at 5 to 6 bits per parameter on average, and inference speedups of 1.7 to 3.6x relative to FP16 with optimized kernels. Source code is available at https://github.com/IST-DASLab/SLQ.

Michael Helcig, Eldar Kurtic, Dan Alistarh

ETH Z̈urich · ISTA

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

May 2, 2026cs.CV

Colinearity Decay: Training Quantization-Friendly ViTs with Outlier Decay

Low-bit quantization is a practical route for efficiently deploying vision Transformers, yet activation outliers complicate fully quantized deployment. Existing methods either handle quantization post-training or suppress large activations during training; however, aggressively restricting outliers in vision models can lead to a poorer trade-off between full-precision and quantized accuracy. We argue that rather than simply suppressing outliers, the training objective should control the structural amplification that makes them harmful. To this end, we introduce Colinearity-Decay (CD), a structural regularizer for ordered matrix pairs within Transformer blocks. CD penalizes detrimental cross-matrix alignment and mitigates extreme activations without altering the architecture or task loss. Applied as a decoupled update, CD is non-invasive and introduces minimal training overhead. Across ImageNet-1K pre-training, COCO detection, and downstream fine-tuning, CD consistently boosts quantized accuracy across multiple pipelines while preserving, or even improving, full-precision performance. Ultimately, our results demonstrate that structural regularization effectively prepares vision Transformers for low-bit deployment with zero inference-time overhead.

Jin Tong, Guang Liang, Peilin Sun +1

State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing 210023, China · School of Artificial Intelligence, Nanjing University, Nanjing 210023, China · Zhongguancun Academy, Beijing 100094, China

Vision Transformer Activation Outliers Activation Quantization Low-Bit Quantization

May 1, 2026cs.LG

BWLA: Breaking the Barrier of W1AX Post-Training Quantization for LLMs

Large language models (LLMs) have driven major progress in NLP, yet their substantial memory and compute demands still hinder practical deployment. Binarization can compress weights to 1 bit, fundamentally lowering compute and bandwidth cost. However, existing methods cannot address activation heavy tails and thus must keep activations in high precision, preventing true end-to-end acceleration. To overcome this limitation, we propose BWLA (Binarized Weights and Low-bit Activations), the first post-training quantization framework that preserves high accuracy while achieving 1-bit weight quantization together with low-bit activations (e.g., 6 bits). The Orthogonal-Kronecker Transformation (OKT) learns an orthogonal mapping via EM minimization, converting unimodal weights into symmetric bimodal forms while suppressing activation tails and incoherence. The Proximal SVD Projection (PSP) then performs lightweight low-rank refinement through proximal SVD projection, further enhancing quantizability with minimal overhead. On Qwen3-32B, BWLA reaches a Wikitext2 perplexity of 11.92 under 6-bit activations (vs. 38 from SOTA), improves five zero-shot tasks by more than 70%, and delivers 3.26 times inference speedup, demonstrating strong potential for real-world LLM compression and acceleration.

Zhixiong Zhao, Zukang Xu, Dawei Yang

1Houmo AI

LLM Quantization LLM Inference Acceleration Activation Quantization Post-Training Quantization Low-Bit Quantization

Apr 30, 2026cs.LG

Technical Report: Activation Residual Hessian Quantization (ARHQ) for Low-Bit LLM Quantization

We present Activation Residual Hessian Quantization (ARHQ), a post-training weight splitting method designed to mitigate error propagation in low-bit activation-weight quantization. By constructing an input-side residual Hessian from activation quantization residuals (G_x), ARHQ analytically identifies and isolates error-sensitive weight directions into a high-precision low-rank branch. This is achieved via a closed-form truncated SVD on the scaled weight matrix W G^{1/2}_x . Experimental results on Qwen3-4B-Thinking-2507 demonstrate that ARHQ significantly improves layer-wise SNR and preserves downstream reasoning performance on ZebraLogic even under aggressive quantization. The code is available at https://github.com/BeautMoonQ/ARHQ.

YiFeng Wang, Zhun Sun, Keisuke Sakaguchi

Graduate School of Information Sciences Tohoku University

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

Apr 29, 2026cs.LG

CoQuant: Joint Weight-Activation Subspace Projection for Mixed-Precision LLMs

Post-training quantization (PTQ) has become an important technique for reducing the inference cost of Large Language Models (LLMs). While recent mixed-precision methods improve ultra-low bit quantization by preserving critical subspaces in high precision, they typically construct these subspaces relying solely on activation statistics. This ignores the fundamental nature of linear operations, where the output perturbation is jointly driven by both activation and weight quantization noise. In this paper, we propose CoQuant, a joint weight-activation subspace projection method. By theoretically modeling the expected output error, CoQuant formulates a closed-form weighted PCA solution that balances activation and weight covariances to select the optimal high-precision subspace. Extensive experiments on Llama-3.2 and Qwen2.5 models show that CoQuant consistently outperforms strong PTQ baselines in both WikiText perplexity and zero-shot common-sense reasoning accuracy. These results demonstrate that joint weight-activation subspace modeling provides a principled and effective direction for low-bit LLM quantization. The source code is available at https://github.com/Zachary5895/CoQuant.

Zhe Ding, Su Pan, Duowei Pan

School of Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing, China · Amazon AGI, Seattle, WA, USA

Mixed-Precision Quantization LLM Quantization Activation Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Apr 28, 2026cs.LG

QFlash: Bridging Quantization and Memory Efficiency in Vision Transformer Attention

FlashAttention improves efficiency through tiling, but its online softmax still relies on floating-point arithmetic for numerical stability, making full quantization difficult. We identify three main obstacles to integer-only FlashAttention: (1) scale explosion during tile-wise accumulation, (2) inefficient shift-based exponential operations on GPUs, and (3) quantization granularity constraints requiring uniform scales for integer comparison. To address these challenges, we propose \textit{QFlash}, an end-to-end integer FlashAttention design that performs softmax entirely in the integer domain and runs as a single Triton kernel. On seven attention workloads from ViT, DeiT, and Swin models, QFlash achieves up to 6.73

\times

speedup over I-ViT and up to 8.69

\times

speedup on Swin, while reducing energy consumption by 18.8% compared to FP16 FlashAttention, without sacrificing Top-1 accuracy on ViT/DeiT and remaining competitive on Swin under per-tensor quantization. Our code is publicly available at https://github.com/EfficientCompLab/qflash.

Sehyeon Oh, Yongin Kwon, Jemin Lee

University of Science and Technology, Daejeon, Republic of Korea · Electronics and Telecommunications Research Institute, Daejeon, Republic of Korea · Pusan National University, Busan, Republic of Korea +1

Softmax Attention GPU Acceleration Vision Transformer Efficient ViTs Attention Quantization Attention Mechanisms+2

Apr 27, 2026cs.LG

BitRL: Reinforcement Learning with 1-bit Quantized Language Models for Resource-Constrained Edge Deployment

The deployment of intelligent reinforcement learning (RL) agents on resource-constrained edge devices remains a fundamental challenge due to the substantial memory, computational, and energy requirements of modern deep learning systems. While large language models (LLMs) have emerged as powerful architectures for decision-making agents, their multi-billion parameter scale confines them to cloud-based deployment, raising concerns about latency, privacy, and connectivity dependence. We introduce BitRL, a framework for building RL agents using 1-bit quantized language models that enables practical on-device learning and inference under severe resource constraints. Leveraging the BitNet b1.58 architecture with ternary weights (-1, 0, +1) and an optimized inference stack, BitRL achieves 10-16x memory reduction and 3-5x energy efficiency improvements over full-precision baselines while maintaining 85-98 percent of task performance across benchmarks. We provide theoretical analysis of quantization as structured parameter perturbation, derive convergence bounds for quantized policy gradients under frozen-backbone architectures, and identify the exploration-stability trade-off in extreme quantization. Our framework systematically integrates 1-bit quantized language models with reinforcement learning for edge deployment and demonstrates effectiveness on commodity hardware.

Md. Ashiq Ul Islam Sajid, Mohammad Sakib Mahmood, Md. Tareq Hasan +3

Department of Computer Science BRAC University Dhaka 1212, Bangladesh · Department of Computer Science Missouri State University Springfield, MO, USA · Department of Computer Science & Engineering Prime University Dhaka, Bangladesh +2

LLM Quantization RL for Language Models On-Device Language Model Inference Edge ML Low-Bit Quantization

Apr 22, 2026cs.CV

Efficient INT8 Single-Image Super-Resolution via Deployment-Aware Quantization and Teacher-Guided Training

Efficient single-image super-resolution (SISR) requires balancing reconstruction fidelity, model compactness, and robustness under low-bit deployment, which is especially challenging for x3 SR. We present a deployment-oriented quantized SISR framework based on an extract-refine-upsample design. The student performs most computation in the low-resolution space and uses a lightweight re-parameterizable backbone with PixelShuffle reconstruction, yielding a compact inference graph. To improve quality without significantly increasing complexity, we adopt a three-stage training pipeline: Stage 1 learns a basic reconstruction mapping with spatial supervision; Stage 2 refines fidelity using Charbonnier loss, DCT-domain supervision, and confidence-weighted output-level distillation from a Mamba-based teacher; and Stage 3 applies quantization-aware training directly on the fused deploy graph. We further use weight clipping and BatchNorm recalibration to improve quantization stability. On the MAI 2026 Quantized 4K Image Super-Resolution Challenge test set, our final AIO MAI submission achieves 29.79 dB PSNR and 0.8634 SSIM, obtaining a final score of 1.8 under the target mobile INT8 deployment setting. Ablation on Stage 3 optimization shows that teacher-guided supervision improves the dynamic INT8 TFLite reconstruction from 29.91 dB/0.853 to 30.0003 dB/0.856, while the fixed-shape deployable INT8 TFLite artifact attains 30.006 dB/0.857.

Pham Phuong Nam Nguyen, Nam Tien Le, Thi Kim Trang Vo +1

University of Information Technology · 3Vietnam National University, Ho Chi Minh City · 2Ho Chi Minh City University of Technology

Efficient Neural Network Inference Quantization-Aware Training Low-Bit Quantization Image Super-Resolution

Apr 21, 2026cs.CL

From Signal Degradation to Computation Collapse: Uncovering the Two Failure Modes of LLM Quantization

Post-Training Quantization (PTQ) is critical for the efficient deployment of Large Language Models (LLMs). While 4-bit quantization is widely regarded as an optimal trade-off, reducing the precision to 2-bit usually triggers a catastrophic ``performance cliff.'' It remains unclear whether the underlying mechanisms differ fundamentally. Consequently, we conduct a systematic mechanistic analysis, revealing two qualitatively distinct failure modes: Signal Degradation, where the computational patterns remain intact but information precision is impaired by cumulative error; and Computation Collapse, where key components fail to function, preventing correct information processing and destroying the signal in the early layers. Guided by this diagnosis, we conduct mechanism-aware interventions, demonstrating that targeted, training-free repair can mitigate Signal Degradation, but remains ineffective for Computation Collapse. Our findings provide a systematic diagnostic framework for PTQ failures and suggest that addressing Computation Collapse requires structural reconstruction rather than mere compensation.

Chenxi Zhou, Pengfei Cao, Jiang Li +4

School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences · The Key Laboratory of Cognition and Decision Intelligence for Complex Systems, Institute of Automation, Chinese Academy of Sciences · College of Computer Science, Inner Mongolia University +1

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

Apr 21, 2026cs.LG

Revisiting RaBitQ and TurboQuant: A Symmetric Comparison of Methods, Theory, and Experiments

This technical note revisits the relationship between RaBitQ and TurboQuant under a unified comparison framework. We compare the two methods in terms of methodology, theoretical guarantees, and empirical performance, using a reproducible, transparent, and symmetric setup. Our results show that, despite the claimed advantage of TurboQuant, TurboQuant performs worse than RaBitQ in most tested settings of inner-product estimation, nearest-neighbor search and KV cache quantization. We further find that several reported runtime and recall results in the TurboQuant paper could not be reproduced from the released implementation under the stated configuration. Overall, this note clarifies the shared structure and genuine differences between the two lines of work, while documenting reproducibility issues in the experimental results reported by the TurboQuant paper.

Jianyang Gao, Yutong Gou, Yuexuan Xu +5

ETH Zurich · Nanyang Technological University · University of Michigan +2

Vector Quantization KV-Cache Quantization Low-Bit Quantization Approximate Nearest Neighbor Search

Apr 21, 2026cs.LG

LBLLM: Lightweight Binarization of Large Language Models via Three-Stage Distillation

Deploying large language models (LLMs) in resource-constrained environments is hindered by heavy computational and memory requirements. We present LBLLM, a lightweight binarization framework that achieves effective W(1+1)A4 quantization through a novel three-stage quantization strategy. The framework proceeds as follows: (1) initialize a high-quality quantized model via PTQ; (2) quantize binarized weights, group-wise bitmaps, and quantization parameters through layer-wise distillation while keeping activations in full precision; and (3) training learnable activation quantization factors to dynamically quantize activations to 4 bits. This decoupled design mitigates interference between weight and activation quantization, yielding greater training stability and better inference accuracy. LBLLM, trained only using 0.016B tokens with a single GPU, surpasses existing state-of-the-art binarization methods on W2A4 quantization settings across tasks of language modeling, commonsense QA, and language understanding. These results demonstrate that extreme low-bit quantization of LLMs can be both practical and highly effective without introducing any extra high-precision channels or rotational matrices commonly used in recent PTQ-based works, offering a promising path toward efficient LLM deployment in resource-limited situations.

Siqing Song, Chuang Wang, Yong Lang +2

MAIS, Institute of Automation, Chinese Academy of Sciences, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, China · Central Media Technology Institute, Huawei

LLM Quantization Activation Quantization Post-Training Quantization Low-Bit Quantization

Apr 20, 2026cs.CL

GSQ: Highly-Accurate Low-Precision Scalar Quantization for LLMs via Gumbel-Softmax Sampling

Quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier but are notoriously hard to implement and to scale. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized

\textit{scalar}

quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus remains compatible with existing scalar inference kernels. We further show that the same discrete-assignment optimization can be applied to practical GGUF K-Quant checkpoints: starting from publicly released GGUF models, GSQ improves accuracy while projecting the result back into the same deployment format. Finally, GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply. The source code is publicly available at https://github.com/IST-DASLab/GSQ.

Alireza Dadgarnia, Soroush Tabesh, Mahdi Nikdan +4

ISTA · ETH Zürich · ISTA & Red Hat AI +1

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

Apr 20, 2026cs.LG

A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work

This note clarifies the relationship between the recent TurboQuant work and the earlier DRIVE (NeurIPS 2021) and EDEN (ICML 2022) schemes. DRIVE is a 1-bit quantizer that EDEN extended to any

b>0

bits per coordinate; we refer to them collectively as EDEN. First, TurboQuant

_{\text{mse}}

is a special case of EDEN obtained by fixing EDEN's scalar scale parameter to

S=1

. EDEN supports both biased and unbiased quantization, each optimized by a different

S

(chosen via methods described in the EDEN works). The fixed choice

S=1

used by TurboQuant is generally suboptimal, although the optimal

S

for biased EDEN converges to

1

as the dimension grows; accordingly TurboQuant

_{\text{mse}}

approaches EDEN's behavior for large

d

. Second, TurboQuant

_{\text{prod}}

combines a biased

(b-1)

-bit EDEN step with an unbiased 1-bit QJL quantization of the residual. It is suboptimal in three ways: (1) its

(b-1)

-bit step uses the suboptimal

S=1

; (2) its 1-bit unbiased residual quantization has worse MSE than (unbiased) 1-bit EDEN; (3) chaining a biased

(b-1)

-bit step with a 1-bit unbiased residual step is inferior to unbiasedly quantizing the input directly with

b

-bit EDEN. Third, some of the analysis in the TurboQuant work mirrors that of the EDEN works: both exploit the connection between random rotations and the shifted Beta distribution, use the Lloyd-Max algorithm, and note that Randomized Hadamard Transforms can replace uniform random rotations. Experiments support these claims: biased EDEN (with optimized

S

) is more accurate than TurboQuant

_{\text{mse}}

, and unbiased EDEN is markedly more accurate than TurboQuant

_{\text{prod}}

, often by more than a bit (e.g., 2-bit EDEN beats 3-bit TurboQuant

_{\text{prod}}

). We also repeat all accuracy experiments from the TurboQuant paper, showing that EDEN outperforms it in every setup we have tried.

Ran Ben-Basat, Yaniv Ben-Itzhak, Gal Mendelson +3

UCL and Broadcom · VMware Research by Broadcom · North Carolina State University +2

Residual VQ Vector Quantization Low-Bit Quantization Neural Network Quantization

Apr 19, 2026cs.CV

Towards Joint Quantization and Token Pruning of Vision-Language Models

Deploying Vision-Language Models (VLMs) under aggressive low-bit inference remains challenging because inference cost is dominated by the long visual-token prefix during prefill and the growing KV cache during autoregressive decoding. Token pruning and low-bit quantization are complementary for reducing these costs, yet naive stage-wise combinations are often brittle due to a mismatch between quantization calibration and pruning execution. We present a collaborative quantization-and-pruning framework that unifies low-bit inference and deterministic visual-token pruning in a single deployable pipeline. The framework introduces the \textbf{Q}uantization \textbf{U}nified \textbf{O}ffline \textbf{T}oken \textbf{A}llocator (\textbf{QUOTA}), which converts low-bit calibration signals into a layer-wise token allocation schedule and materializes it as a pruning recipe. Token importance is evaluated under deployed W4A4 operators with a quantized KV cache by combining activation magnitude, attention cues, and an explicit low-bit risk signal, enabling consistent budgeted top-

k

selection. Experiments on standard VLM benchmarks show improved robustness over stage-wise baselines under the same low-bit regime, achieving 95.65% average retention while retaining only 30% of visual tokens, compared with about 94.3% retention for representative stage-wise combinations. The code will be released.

Xinqing Li, Xin He, Xindong Zhang +3

VCIP, College of Computer Science, Nankai University · School of Computer Science and Engineering, Tianjin University of Technology · OPPO Research Institute +3

Vision-Language Models VLM Quantization Efficient VLM Inference Low-Bit Quantization Visual Token Pruning Neural Network Compression

Apr 15, 2026cs.LG

Robust Ultra Low-Bit Post-Training Quantization via Stable Diagonal Curvature Estimate

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

Jaemin Kim, Sungkyun Kim, Junyeol Lee +1

Seoul National University · Hanyang University

LLM Quantization Language Model Calibration Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Feb 3, 2026cs.LG

MatGPTQ: Efficient and Accurate Inference over Nested Quantized Models

Matryoshka Quantization (MatQuant), Any-Precision-LLM (AP) and AnyBCQ (AB) are recent quantization approaches showing that a single integer-quantized model can be served across multiple precisions. In this paradigm, lower-precision models are extracted from a higher-precision model by simply reading fewer bits of the weights. This enables a single checkpoint to cover a wide range of memory and latency budgets, but makes both quantization and efficient execution substantially harder. Existing methods rely on expensive quantization-aware training (QAT) or gradient-based post-training quantization (PTQ) rather than fast one-shot PTQ, and offer limited system support: dedicated kernels are either missing or restricted to single- or small-batch decoding. We address these limitations with Post-Training Matryoshka Quantization (MatGPTQ), an end-to-end pipeline for nested-model quantization and inference. MatGPTQ casts Matryoshka quantization as multi-precision error compensation, producing a single "sliceable" parent model jointly optimized for multiple target precisions in one pass over a small calibration set. We further refine the MatQuant representation so that an

r

-bit model reads exactly

r

bits, and introduce the first dedicated inference kernels for this format, supporting batch sizes beyond one and integrated into vLLM. Across standard LLMs and benchmarks, MatGPTQ outperforms MatQuant while remaining competitive with AP and AB at the smallest checkpoint size, and our kernels achieve end-to-end speedups of up to 3.5

\times

over BF16 at the low-bit regime. Overall, MatGPTQ makes nested quantized models practical to serve from a single, compact checkpoint. Code is available at https://github.com/IST-DASLab/MatGPTQ.

Maximilian Kleinegger, Elvir Crnčević, Dan Alistarh

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

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

Nov 24, 2025cs.LG

QuantKAN: A Unified Quantization Framework for Kolmogorov Arnold Networks

Kolmogorov--Arnold Networks (KANs) replace linear weights with spline-based functions, offering strong expressivity but posing challenges for low-precision deployment due to heterogeneous parameter distributions. We introduce QuantKAN, the first unified framework for quantization-aware training (QAT) and post-training quantization (PTQ) of KANs. The framework employs branch-aware quantizers for base and spline parameters and extends modern QAT and PTQ methods to spline-based layers across EfficientKAN, FastKAN, PyKAN, and KAGN. Experiments on MNIST, CIFAR-10/100, TinyImageNet, and ImageNet provide the first unified QAT/PTQ KAN benchmarks and show that DSQ is the most robust QAT method at aggressive low-bit settings, while GPTQ is the strongest PTQ method at moderate precision. Sensitivity analyses reveal architecture-specific failure modes: spline/basis parameters dominate in FastKAN, while base or scaling parameters dominate in EfficientKAN, GRAM, and PyKAN. Vivado HLS estimates on a Xilinx UltraScale+ device further suggest up to 3.32

\times

throughput and 7.7

\times

lower estimated dynamic energy per inference under W4A4, exposing a residual \emph{basis-evaluation tax} that motivates basis-aware microarchitecture. QuantKAN is available at https://github.com/OSU-STARLAB/QuantKAN/.

Kazi Ahmed Asif Fuad, Lizhong Chen

Department of EECS · Oregon State University · Corvallis, OR 97331

Quantization-Aware Training Kolmogorov-Arnold Networks Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Oct 6, 2025cs.LG

Activation Quantization of Vision Encoders Needs Prefixing Registers

Large pretrained vision encoders are central to multimodal intelligence, powering applications from on-device vision processing to vision-language models. Since these applications often demand real-time processing of massive visual data, reducing the inference cost of vision encoders is critical. Quantization offers a practical path, but it remains challenging even at 8-bit precision due to so-called outliers. In this work, we propose

\textit{RegCache}

, a training-free algorithm that mitigates outliers in large-scale pretrained vision encoders and serves as a plug-in module that can be applied on top of other quantization methods. RegCache introduces outlier-prone yet semantically meaningless prefix tokens to the vision encoder, which prevent other tokens from having outliers. Notably, we observe that outliers in vision encoders behave differently from those in language models, motivating two technical innovations: middle-layer prefixing and token deletion. Experimental results show that our method consistently improves quantized model performance across various vision encoders, particularly in extremely low-bit regimes (e.g., 4-bit).

Seunghyeon Kim, Taesun Yeom, Jinho Kim +3

POSTECH · NYU Langone Health2 · Google3

Activation Outliers Activation Quantization Low-Bit Quantization Neural Network Quantization