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

Oct 7, 2026cs.LG

ResidualQuant: KV Cache Quantization for Looped Transformers with 2-Bit Residuals

Looped Transformers improve parameter efficiency by repeatedly applying shared Transformer blocks over multiple recurrent loops, increasing computational depth without increasing the parameter count. However, KV cache memory still scales with the number of loops, becoming a key memory bottleneck that limits batch size and inference throughput. KV cache quantization can alleviate this bottleneck, but existing methods often suffer substantial accuracy degradation at aggressive low-precision regimes. We observe that looped Transformers offer a unique opportunity: KV states across loops are highly similar. Based on this observation, we propose ResidualQuant, which uses the final-loop KV states as a reference and represents the remaining loops with low-precision residuals. Our method further combines least-square scaling and rotations applied to the residuals, as well as loop-wise mixed precision, to enable accurate quantization down to INT2 while retaining efficient reconstruction. Across multiple looped Transformer models and mathematical reasoning and code generation benchmarks, ResidualQuant consistently improves the accuracy-memory tradeoff over state-of-the-art rotation-based KV quantization. In particular, our method retains accuracy close to BF16 under mixed-precision settings while reducing theoretical KV storage by 80.7%, achieving up to 13.0% higher accuracy than the rotation-based baseline at the same memory budget. On an RTX 5090, the reduced KV memory traffic improves fixed-batch decode throughput by up to 2.73x, while the smaller memory footprint enables up to 2x larger batches, improving peak throughput by up to 4.15x.

Heejun Kim, Junyoung Lee, SangLyul Cho +3

KAIST · Yonsei University · Seoul National University

KV-Cache Quantization Efficient Transformer Inference Low-Bit Quantization Recurrent Transformers

Oct 7, 2026cs.LG

Dual-QK: Sharp Queries and Flat Keys for Prunable 2-bit KV Caches

Long inputs and extended generation increase the storage and access costs of the key-value (KV) cache. Low-bit quantization reduces storage and memory traffic, while query-channel pruning can further reduce key-cache reads. Rotation-based quantization redistributes the energy of key outliers across channels. To maintain computational invariance, the same orthogonal transform must be applied to queries, preserving query-key dot products. However, this rotation can disperse query energy, weakening the separation between a few large components to retain and many small ones to prune. We introduce Dual-QK, which uses paired non-orthogonal query and key transforms to address this conflict. Using calibrated query and key statistics, Dual-QK combines partial key whitening with a query-aligned basis to balance key scales for INT2 quantization and concentrate query energy for dynamic channel pruning. Channel-0 protection and bucket-relative RoPE support low-bit accuracy over long contexts. Experiments on four models across five generative benchmarks and long-context retrieval tasks show improved accuracy over OSCAR on most tasks at 40% query-channel sparsity. At a 128K context, Dual-QK provides

6.8\times

KV-cache compression and an estimated

8.3\times

reduction in KV read volume relative to unpruned BF16. Under the evaluated configurations, our SGLang implementation achieves up to

3.75\times

the decoding throughput of unpruned BF16.

Sunjoo Whang, Jungjun Oh, Minsung Kim +5

KAIST · GIST · Google Research

KV-Cache Compression KV-Cache Quantization KV-Cache Pruning Low-Bit Quantization

Oct 6, 2026cs.LG

CurveTQ: Rotation-Free Trellis Quantization of LLM Weights via Curvature-Weighted Search

The best two-bit weight quantizers for large language models, such as QTIP and Proteus, rotate each weight matrix by a random orthogonal transform, which must be undone at every decoding step, then encode it with a trellis or lattice code under a Euclidean search; the layer Hessian enters only through error feedback between coding blocks. We show that this leaves part of the Hessian unused. Error feedback turns the loss into a weighted sum of per-coordinate rounding errors whose weights, the diagonal of the Hessian's LDL factorization, existing quantizers compute but never read. We put these weights into the Viterbi branch metric, so the search follows the curvature within each coding block. This also explains the rotation: it removes this within-block variation, so weighting in the native basis and rotating are substitutes. On three models the weighted native search matches a full-dimension randomized Hadamard to within about one point of downstream accuracy, and weighting after the rotation gains little. Around this search we build CurveTQ, a trellis codec with no rotation, which handles the weights' amplitude and marginal shape with a factored scale field and a closed-form quantile table, and stores a start state per coding block so the trellis can adapt to the residual that error feedback carries into it. At two bits CurveTQ is 1-3 points higher in mean downstream accuracy than QTIP and Proteus on three 4-8B Instruct models, even after both are given our start state, which alone lifts either baseline by 1-3 points. It also leads on a 35B mixture of experts, to our knowledge the first trellis-coded result on such a model. With no rotation to undo, our decoder is the fastest of the three at all tested batch sizes and bit widths.

Guanhua Ding, Zi Wang, Ruichao Li +1

Black Sesame Technologies

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

Oct 6, 2026cs.AI

Few Bits, One Law: Toward W2A4KV2

Extreme low-bit LLM compression is most challenging when weights, activations, and KV caches are quantized together: their distributions differ, and quantization errors interact throughout the network. We introduce CanonQ, a unified quantization-aware training framework that addresses these challenges by separating source canonicalization from task-aware adaptation. Fixed rotations and energy normalization map heterogeneous tensor sources to canonical coordinates, enabling frozen Gaussian-reference codebooks to be reused across layers and models. Joint training then adapts the network to the coupled errors of weight, activation, and cache quantization within a common scalar/vector interface. We bound frozen-codebook transfer error and local task loss, and derive an exact normalization-aware straight-through Jacobian that links quantization distortion to gradient bias. The strongest gains arise under joint W2A4KV2 compression: across LLaMA3-1B/3B/8B, CanonQ-Omni achieves up to 14.28x lower WikiText-2 perplexity and up to 57.9% higher mean zero-shot accuracy than prior state-of-the-art and representative quantization baselines. The benefits extend to Qwen3-1.7B, code generation, and mathematical reasoning: on instruction-tuned MobileLLM-Pro-1B at W2A16KV16, CanonQ achieves relative improvements of 41.7% in HumanEval pass@1 and 39.1% in GSM8K exact match over the strongest evaluated quantization baseline.

Kai Yi, Tarek Elgamal, Sruthikesh Surineni +3

Meta AI

LLM Quantization Low-Bit Quantization Neural Network Quantization Quantization-Aware Training KV-Cache Quantization Activation Quantization

Oct 6, 2026cs.LG

Align, Then Correct: Training-Free Two-Stage Low-Rank Compensation for Extremely Quantized Large Language Models

Low-rank quantization error compensation (LQEC) recovers the accuracy lost under aggressive weight quantization by attaching a closed-form rank-

r

adapter beside each frozen quantized weight, without any training. We show that existing compensators are limited by two shared simplifications. They calibrate symmetrically, evaluating the full-precision and compensated weights on the same activation, which yields a compensation target that is inherently high-rank -- so a fixed rank budget captures only a small fraction of it. And they minimize only the second-order term of the loss, although the compensated model is not stationary: a first-order descent direction larger than the applied compensation itself remains in every layer, and no reconstruction objective can absorb it. We propose a two-stage closed-form framework that removes both simplifications. Stage 1 aligns each layer's output with the full-precision model under a Fisher-weighted asymmetric objective, concentrating the rank budget on a rank-compressible target. Stage 2 re-measures statistics on the compensated model and applies a rank-constrained natural-gradient step that absorbs the remaining first-order signal. Every adapter is the result of a single truncated SVD; backward passes serve only to collect statistics. At 2 bits under QuIP#, our method reduces WikiText-2 perplexity from 12.43 to 10.26 on Qwen3-8B and from 21.11 to 13.22 on Qwen3-4B. On the held-out C4 corpus, it recovers 51% and 84% of the gap to FP16, versus 31% and 63% for the strongest baseline, with consistent gains in the seven-task zero-shot average, at higher bit-widths, and under a distinct quantizer.

Seobin Song, Geonho Lee, Janghwan Lee +1

Hanyang University, Seoul, Republic of Korea · Qualcomm AI Research, Qualcomm Korea YH, Seoul, Republic of Korea

LLM Quantization Post-Training Quantization Low-Bit Quantization

Oct 6, 2026cs.LG

ApexQuant: Data-Free Elastic Quantization by Residual Re-Isotropization

We introduce ApexQuant, a calibration-free quantization method that recursively re-quantizes the residual error, serving as a refinement layer on top of existing quantizers. We establish that a fresh random rotation returns each residual to the uniform distribution on the hypersphere, which characterizes the rate of progressive error decay across successive passes. This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error. Every prefix is itself a valid lower-rate model, so one artifact serves several precisions. We instantiate ApexQuant with three interchangeable stages, scalar,

E_8

and trellis, and validate it on four open-weight LLMs and on Earth-observation and medical domains where in-distribution data is often unattainable as imagery arrives under restrictive licences or due to patient material under privacy constraints. Progressive re-isotropization comes within a few percent of full precision at four bits and gives the best two-bit arm we measure, in a completely data-free setting.

Aksel Fristrup, Sumit Pandey, Ankit Kariryaa

Henselian (henselian.com) · Department of Computer Science University of Copenhagen Denmark · Towards Deep Learning

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

Oct 5, 2026cs.LG

StagQ: Constraint-Driven Multi-Precision Weight Quantization for LLMs

Serving a large language model (LLM) across a fleet of deployments requires several weight-precision operating points. Multi-precision formats serve them all from one stream whose prefixes are valid lower-precision codes, instead of storing multiple copies. We present StagQ, a multi-precision weight format whose main stream is a 2-bit group-wise affine base followed by a configurable number of 1-bit refinement planes on a dyadic step schedule. Every supported precision is a readable prefix, decoded by an affine map derived from metadata shared across all precisions, with no per-weight lookup. A sparse side record, filled both before and after the grid is fitted, holds out the few weights the grid serves worst. We report two configurations of the encoder. At two bits the cheaper one leads the strongest multi-precision baseline on Llama-3.1-8B, Phi-4, and OLMo-2-7B by 3.1 to 7.0 MMLU points, at a slightly lower logical rate. At three bits it leads on Llama-3.1-8B, leads on Phi-4 at a higher rate, and ties on OLMo-2-7B. At four bits it ties on all three, at a higher rate. In a batch-one matrix-vector product on an NVIDIA A100 GPU, timed on synthetic weights, our kernel is faster than the two baseline kernels in most shape-precision cases.

Zhe Wei, Mengqi Guo, Yuan Yuan +3

Huawei Technologies Ltd.

Mixed-Precision Quantization LLM Quantization Weight-Only Quantization Low-Bit Quantization

Oct 4, 2026cs.LG

Loopy: Low-Bit Quantization Framework for Looped Language Models

Looped language models provide a parameter-efficient way to scale iterative test-time computation by repeatedly executing a shared recurrent core. Post-training quantization (PTQ) can reduce the memory footprint and inference cost of looped language models, but errors introduced by a quantized shared core affect subsequent cores. Among PTQ methods, channel scaling and orthogonal rotations preserve the floating-point computation while producing representations with different quantization quality. We find that quantization configuration candidate rankings can change with recurrent depth, motivating configuration selection at the target deployment depth. However, evaluating every candidate over the full calibration set at this depth is costly. We therefore propose Loopy, a PTQ framework that formulates shared-core quantization through a recurrent-depth-aware objective, selecting shared low-bit representations by their final prediction loss at the target deployment depth. Channel scaling and orthogonal rotations parameterize the candidate representations. To approximately solve this selection problem efficiently, Loopy progressively allocates calibration windows to promising candidates while preserving complete target-depth execution, using only forward evaluations. Across eight settings, Loopy achieves the state-of-the-art results among different baselines. On Ouro-1.4B under W4A4, Loopy reduces LAMBADA perplexity by 36.5% relative to SpinQuant. Our code is available at https://github.com/Shameless0817/Loopy-review.git.

Zeyu LI, Yipu ZHANG, Jintao Chen +2

The Hong Kong University of Science and Technology · Duke Kunshan University

LLM Quantization Post-Training Quantization Low-Bit Quantization Recursive Language Models

Oct 1, 2026cs.LG

Stochastic Rounding in Low-Precision Transformer Inference: A Variable-Precision Emulation Study of a Small GPT-2

Should low-precision transformer inference use stochastic rounding (SR) or round-to-nearest (RN)? The answer depends on where in the network you look. We isolate this effect by holding the numerical format fixed and varying only the rounding rule at individual operation sites. To enable experiments at freely chosen precisions, we extend the PRISM vectorized rounding library to arbitrary virtual precision via a variable-precision stochastic rounding (VPSR) algorithm, proving that the rounding decision is evaluated exactly in hardware floating point. We develop two analyses providing complementary insight into this site-level trade-off. First, a probabilistic forward-error bound for linear projections shows that SR's error envelope grows as

O(\sqrt{n} u)

in reduction length

n

, versus

O(n u)

for RN, a gap that widens rapidly at low precision and is most pronounced in the long multilayer perceptron (MLP) down-projection. Second, a second-order decomposition of expected cross-entropy loss change at the output softmax into signed drift, drift curvature, and a Fisher-weighted variance penalty reveals why the two sites behave oppositely: MLP noise is predominantly a uniform logit shift to which softmax is invariant, so SR's variance is largely discounted; head noise is non-uniform across the vocabulary and is not. On DistilGPT-2 at

t=6

significand bits, observations match theory: SR in the MLP raises perplexity to 1.15x the full-precision reference, versus 2.21x for RN. At the language-model head, the ordering reverses because SR introduces non-uniform variance, whereas deterministic RN carries none. In a mixed-precision configuration (MLP output at

t=6

), assigning SR to the MLP and RN to the head brings perplexity within 1.10x of the full-precision reference, a 28% reduction over matched-bit RN.

Yohan Chatelain, Pablo de Oliveira Castro

Krembil Centre for Neuroinformatics, CAMH, Toronto, Canada · Université Paris-Saclay, UVSQ, LI-PaRAD Versailles, France · Universite Paris-Saclay, UVSQ, LI-PaRAD, Versailles, France

Transformer Inference Low-Bit Quantization

Sep 30, 2026math.OC

Q-MINO: A Minimal-Norm Method for Quantization-Aware Training

The Straight-Through Estimator (STE) is a widely used heuristic for Quantization-Aware Training (QAT), but its surrogate gradients can exhibit substantial mismatch with the underlying quantized objective, leading to noisy updates and parameter oscillations, particularly in ultra-low-bit regimes. We propose the Quantization-Aware Minimal-Norm Optimizer (Q-MINO), a temporal bundle method that combines gradient consensus, state-drift regularization, and an alignment constraint to construct stabilized, minimum-norm update directions from recent optimization states. Q-MINO solves the resulting constrained subproblem using a warm-started Frank--Wolfe procedure with a feasible fallback initialization. Theoretically, via a stochastic Lyapunov Kurdyka--Łojasiewicz (KL) framework, we show that Q-MINO achieves asymptotic neighborhood convergence. Moreover, we detail numerical experiments with Q-MINO at various quantizations.

Don Li

Department of Mathematics & Statistics Portland State University

Quantization-Aware Training Low-Bit Quantization

Sep 30, 2026cs.LG

XOR-Trellis: Ultra-Low-Complexity Dequantization and Curvature-Aware Hadamard-Free LLM Quantization

Trellis-coded quantization enables high-dimensional compression of large language model (LLM) weights at ultra-low bit widths without the exponentially large codebooks required by conventional vector quantization. Practical deployment, however, presents two challenges: reconstructing compressed weights at sufficient parallel throughput to avoid making dequantization an inference bottleneck, and maintaining quantization accuracy without costly incoherence transformations. We address these challenges with two complementary techniques. First, we introduce an ultra-low-complexity trellis dequantizer that uses a structured, hardware-efficient state-to-value mapping while preserving diverse reconstruction choices for trellis search. Second, we reformulate discrete trellis path optimization with a curvature-aware objective that reflects model sensitivity directly in the original coordinate space. Together, these techniques enable high-quality ultra-low-bit trellis quantization with inexpensive, highly parallel runtime reconstruction and without relying on Hadamard-based incoherence processing.

Xiaofan Que, Nir Elkayam, Spandan Pyakurel +2

Arm, Inc. · Rochester Institute of Technology

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

Sep 30, 2026cs.LG

Beyond Accuracy: Prefix-Invariant Realizations of Low-Precision Fast Matrix Multiplication

Fast matrix multiplication saves multiplications through exact cancellation, but rounding sums that mix token rows can leave contributions from later tokens in earlier language model outputs. This threatens prefix invariance, which multiple-choice likelihood scoring relies on: a scored likelihood must depend only on its allowed prefix. On Qwen2.5-14B-Instruct, two fast FP8 realizations repaired to ordinary-looking accuracy still change the answers chosen by likelihood on 5.83% and 10.00% of 240 OpenBookQA items when only the text after the allowed prefix is replaced with the bf16 model's own greedy continuation. Both row-local controls, the bf16 model and a deployed FP8 matrix multiplication kernel, change none. Accuracy thus does not certify prefix invariance, and the stability criteria we analyze cannot tell realizations apart: across all 512 sign variants of two-level Strassen they stay constant while teacher-forced perplexities span a 772.4

\times

range on the same model. We therefore construct certified realizations of two-level Strassen on bounded integer codes that quantize token rows independently, then mix and cancel exactly before rescaling, using 49 block multiplications instead of 64. Our certificate guarantees bitwise equality to a prescribed row-local classical int8 operator at the same quantization specification, so every certified realization inherits its prefix invariance. Certification thus turns realization choice into a pure cost decision: which certified realization runs can no longer change a single scored likelihood.

Shuxiao Xie, Shuyang Xie, Yuan Cao +3

LLM Inference Acceleration Low-Bit Quantization

Sep 29, 2026cs.LG

ShamAN-Q: Shampoo Augmented NanoQuant for Sub-1-bit LLM Weights

We introduce ShamAN-Q, a sub-1-bit post-training quantization method that extends NanoQuant by replacing each its diagonal reconstruction geometry with a tractable dense curvature metric, using a general paradigm popularized by the Shampoo optimizer. For each linear weight, ShamAN-Q fits a Kronecker product to the empirical Fisher information matrix of a small calibration set by Kullback--Leibler minimization, forming a Mahalanobis reconstruction loss from the result. The continuous ADMM updates from NanoQuant become solutions to Sylvester equations, while its discrete projection and deployment format remain unchanged. Because the curvature is local to a given set of weights, ShamAN-Q re-measures the input curvature statistic for each layer immediately before layer factorization, periodically refreshing all statistics on the partially quantized model. ShamAN-Q also redistributes the uniform rank from NanoQuant across layers at the same total number of bits. On Qwen3-Base, ShamAN-Q lowers WikiText-2 perplexity at

\approx

1 bpw from 27.56 to 22.96 (0.6B), 19.21 to 16.72 (1.7B), and 14.29 to 13.80 (4B) while matching or improving zero-shot accuracy on the Eleuther LM Evaluation Harness. On 0.6B, ShamAN-Q at

\approx

0.8 bpw matches the published perplexity of NanoQuant at

\approx

1.0 bpw.

Jonathan Mei, Sang Hyub Kim, Oliver Knitter +2

Applications R&D IonQ College Park, MD 20740, USA

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

Sep 29, 2026cs.LG

QuantMLA: Function-Aligned Dual-Path Quantization for Low-Bit MLA KV Caching

Multi-Head Latent Attention (MLA) enables expressive multi-head attention with compact caches for its content and decoupled RoPE paths, yet cache memory still scales linearly with context length and batch size. In this work, we establish a systematic model of MLA's dual-path quantization errors, characterizing their distinct effects on attention-output distortion and explaining the pronounced amplification of RoPE-path errors. Guided by this analysis, we introduce QuantMLA, a function-aligned framework for low-bit dual-path quantization. We derive path-specific transformation spaces that preserve full-precision computation while remaining fully fusible into model parameters offline, eliminating online transformation overhead. Within these spaces, QuantMLA learns path-specific transformations with function-aligned objectives: attention-output reconstruction captures the content path's coupled matching and aggregation errors, while positional QK reconstruction preserves the RoPE-induced component of the attention logits and admits a theoretical bound on output distortion. Across four MLA model families, QuantMLA enables, to our knowledge, the first reported joint INT4 caching of the content and RoPE caches with minimal accuracy degradation. Further compressing the content cache to INT2 while retaining the RoPE key cache at INT4 maintains competitive performance on challenging reasoning and code benchmarks. We develop a native low-bit MLA attention kernel that integrates unpacking and dequantization directly into attention computation. The physical cache layout provides 3.59x compression at 128K context, while a cache-pressure serving workload achieves 5.168x higher whole-job output throughput than BF16. The code will be released upon acceptance.

Zunhai Su, Yuxuan Sun, Jianchao Tan +5

The University of Hong Kong · Meituan LongCat Team · South China University of Technology +1

LLM Inference Acceleration Attention Quantization KV-Cache Quantization Multi-Head Latent Attention Post-Training Quantization Low-Bit Quantization+1

Sep 28, 2026cs.LG

ThinQuant: Scalable Rotation Learning for Weight and Activation Quantization of LLMs

Learned rotations play an important role in enabling low-bit weight and activation quantization of large language models by smoothing outliers in the activation distribution. State-of-the-art approaches include gradient-based procedures such as SpinQuant and computationally friendlier gradient-free approaches such as DartQuant, but both remain hard to scale to the largest architectures. To address the computational bottlenecks in gradient-free rotation learning, we introduce two ideas for efficiency, (i) a data selection procedure which reduces the required number of calibration data points, and (ii) an exact reduction of the associated optimization on this reduced calibration set. Our data selection procedure exploits the geometric structure of the convex hull of the activations. Using this idea, we show that a carefully selected calibration set with several orders of magnitude fewer activations than state-of-the-art rotation-based methods can match their performance in low-bit quantization settings. Under this extreme data efficiency, the selected activations span an

r

-dimensional subspace with

r<d

, making optimization over a

d\times d

rotation equivalent to optimizing a

d\times r

matrix on the Stiefel manifold. We solve this reduced problem using an efficient ADMM algorithm that iteratively employs thin matrix updates at every step, hence the name ThinQuant. For Llama-3-70B with W4A4KV4 quantization, ThinQuant completes the entire rotation calibration in under 12 minutes and achieves a WikiText-2 perplexity of 5.63, compared with 7.55 for DartQuant, which requires 111 minutes. Unlike SpinQuant and DartQuant, ThinQuant also scales to Llama-3.1-405B on a single H200 GPU, completing rotation calibration in just over 2 hours and achieving WikiText-2 perplexity of 2.97 at W4A4, compared with 3.48 for GPTAQ+QuaRoT.

Mehdi Makni, Ryan Lucas, Rahul Mazumder

Operations Research Center Massachusetts Institute of Technology

LLM Quantization Rotation-Based Quantization Activation Quantization Low-Bit Quantization

Sep 28, 2026cs.LG

TORQUE: Optimizing What (not) to Quantize Before and After Rotation

Uniform random rotations are an effective preprocessing step for quantization: they make normalized coordinate distributions approximately Gaussian, enabling the use of codebooks optimized offline. We introduce TORQUE, a framework that improves on previous quantization works that use random rotations by jointly optimizing how many and which coordinates to preserve at high precision both before and after rotation, under a fixed overall expected bit budget. Intuitively, before rotation, preserving large input coordinates at high precision can reduce overall error by preventing the rotation from spreading their values across many coordinates. Likewise, after rotation, preserving a small fraction of the largest-magnitude coordinates at high precision allows the remaining values to be quantized more accurately using codebooks optimized offline for the resulting truncated Gaussian distribution. We derive a quantization error upper bound and prove that top-

k

pre-rotation retention minimizes it for each

k

. This reduces the search over coordinate subsets to an optimization over

k

, enabling a fast optimizer that uses offline codebooks and parallel parameter selection for practical implementation. We demonstrate an improved tradeoff between reconstruction accuracy and storage cost through numerical evaluation under the Gaussian model and experiments on nearest-neighbor retrieval, KV-cache compression, and activation compression.

Ran Ben Basat, Michael Mitzenmacher, Shay Vargaftik

University College London · Harvard University · VMware Research by Broadcom

Rotation-Based Quantization Vector Quantization Activation Quantization Low-Bit Quantization Neural Network Quantization

Sep 28, 2026cs.LG

Tetra: Serving Leech-Lattice Quantized LLMs at 2.7 Bits per Parameter

Leech-lattice quantization gives good quality at two bits per weight, but its codebooks hold more than 10^14 points, too many for a lookup table. Our earlier kernel expanded the codes at load time and read 4.804 bits per weight from GPU memory for 2 bits of code. We present Tetra, a new codebook on the same lattice. A 24-weight block still takes 48 bits, most of which index a 64-state trellis of the Golay code and one shared 16 KiB table. The kernel decodes a block with six table loads and two small lookups inside the matrix-vector product, and reads 2.148 bits per weight. For full models, we retrain one scale per matrix row, store the matrices that lose the most as 4-bit integers, and pay for them with 4-bit embedding tables. Our Qwen3-4B, 8B and 14B files hold 2.73, 2.70 and 2.73 bits per parameter over the whole model. They score 63.37, 69.58 and 75.66 on the full MMLU test set, 4.76, 4.21 and 2.46 points below 4-bit AWQ at 5.3 to 6.0 bits per parameter. They generate 113.8, 95.0 and 57.2 tokens per second in our engine. On GSM8K, through the served kernel, they lose 9.63, 4.62 and 3.26 points to FP16. At 4B our file scores 23.6 points above llama.cpp's IQ2_XXS (2.48 bits per parameter). Every number we measured for a table or figure comes from one NVIDIA L40S GPU. We preregistered the main experiments.

Pier-Jean Malandrino

Scub, Bordeaux, France

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

Sep 28, 2026cs.CV

GLF-Q: Global-Local Feature-based Quantization for Vision Transformers

Post-training quantization (PTQ) efficiently compresses Vision Transformers (ViTs) without retraining, yet suffers severe accuracy degradation at low bit-widths. Existing optimization-based PTQ methods guide block reconstruction via either soft logits or second-order Hessian proxies. Logit supervision is prone to overfitting on limited calibration data, while Hessian approximations incur structural truncation errors. To address these limitations, we propose \textbf{GLF-Q}, a novel PTQ framework guided by Global-Local Feature alignment. GLF-Q propagates quantized block outputs through downstream full-precision layers to align penultimate-layer representations under local output regularization, providing downstream feature supervision without explicitly approximating the Hessian or using a Taylor expansion. Furthermore, offline Hadamard transformations are introduced with zero runtime overhead to disperse activation outliers across channels, effectively contracting dynamic ranges and reducing quantization errors. Meanwhile, optimizing this loss via a Straight-Through Estimator (STE) achieves rapid convergence, bypassing continuous relaxation rounding formulations such as AdaRound. Extensive experiments across representative ViT architectures demonstrate that GLF-Q with standard uniform quantizers substantially outperforms state-of-the-art methods under 3-bit quantization on image classification. In addition, GLF-Q exhibits strong out-of-domain calibration robustness and achieves speedups under 8-bit GPU deployment.

Peilin Sun, Guang Liang, Jin Tong +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

Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Sep 22, 2026cs.LG

Train Where the Quantized Model Goes: On-Policy Distillation for Low-Bit Reasoning

Quantization-aware distillation (QAD) restores much of the short-form question-answering performance lost to sub-3-bit quantization, yet leaves mathematical and code reasoning substantially impaired. Long generations often degenerate into repetitive loops, exhausting the decoding budget without completing a solution. We trace this gap to quantization-amplified exposure bias: QAD trains on fixed corpus prefixes, while quantization-induced deviations compound along the model's own autoregressive trajectories. To address this mismatch, we introduce an on-policy distillation (OPD) stage that places teacher supervision where the quantized model actually goes. Starting from a QAD checkpoint, the student generates through the quantized forward path used at deployment and receives feedback from a frozen full-precision teacher on its own prefixes, combining dense token-level guidance with task-verifier rewards. Across four models at 2.79 and 1.88 effective bits, OPD raises average BF16 performance retention from 35% to 70% on MATH-500 and from 66% to 91% on HumanEval while preserving short-form performance, with reasoning gains substantially exceeding those of continued teacher-forced QAD in matched-budget comparisons. By coupling QAD's stable low-bit initialization with OPD's on-policy reasoning recovery, our framework provides a comprehensive sub-3-bit solution that preserves broad capabilities while restoring long-form reasoning.

Yuanteng Chen, Zhilei Liu, Peisong Wang +7

Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Zhongguancun Academy +2

LLM Quantization Quantization-Aware Training Code Generation Mathematical Reasoning On-Policy Distillation Low-Bit Quantization

Sep 22, 2026cs.CV

QuantWM: Temporally Consistent 2-Bit KV Cache Quantization for Video World Models

Video world models achieve long-range temporal consistency by storing KV cache during generation, but the growing cache makes KV cache memory a major deployment bottleneck, which motivates low-bit quantization study for efficiency. Existing 2-bit KV cache quantization methods can achieve nearly lossless performance on VBench, however, when applied to video world models, we find they still cause severe temporal flickering and visual degradation. Meanwhile, deeper investigates show that Key quantization produces smaller reconstruction errors than Value, but surprisingly leads to larger output degradation. We trace this discrepancy to attention in video world models: Key perturbations can change the attention logits, and shift the temporal-spatial tokens selected by Queries. These observations motivate us to preserve attention logits and temporal-spatial token selection during KV cache quantization. To address this issue, we present QuantWM, a training-free 2-bit KV cache quantization framework for video world models. QuantWM introduces two complementary techniques to mitigate the attention shifts. Firstly, quantization-sensitivity-aware clustering (QSAC) jointly considers historical Query sensitivity and residual ranges to select INT2-friendly Key centroids, which reduces quantization errors in channels that are more critical to attention. In addition, principal-subspace attention compensation (PSAC) restores the remaining Key errors along the dominant Query subspace using low-rank projections, which provides a direct and efficient correction to stabilize attention logits. Experiments on LingBot-World-v2, HY-World 1.5, Matrix-Game-2, Longcat-Video and Causal-Forcing demonstrate that QuantWM significantly improves visual quality and temporal consistency, while outperforming existing methods across benchmarks with up to 6.20 KV cache memory compression and limited additional overhead.

Jiaqi Zhao, Xiaobin Hu, Bo Yin +3

Harbin Institute of Technology (Shenzhen), Shenzhen, China · National University of Singapore, Singapore

KV-Cache Compression KV-Cache Quantization Low-Bit Quantization Temporal Consistency in Video Generation Video World Models

Sep 21, 2026cs.CV

RGSQ: Riemannian Geometry-Sensitive Quantization for Large Vision-Language Models

Large vision-language models (VLMs) can be efficiently deployed under stringent memory and latency constraints through post training quantization (PTQ). However, most PTQ methods are designed for unimodal large language models (LLMs). These methods treat quantization errors as isotropic perturbations under the Euclidean assumption, which provides weak guidance on directions most sensitive to quantization in VLMs. Consequently, directly adapting unimodal PTQ approaches or solely employing modality-specific scaling often leads to uneven bit-width distribution and inconsistent performance in low-bit settings. To address these challenges, we propose Riemannian Geometry-Sensitive Quantization (RGSQ), which formulates quantization as a reconstruction problem under a unified Fisher-Riemannian metric. RGSQ identifies modality-specific sensitive directions via Riemannian manifold mappings built from modality-partitioned empirical Fisher factors and fused into a modality-aware Kronecker-structured metric. We then apply geometry-aligned rotations to reorient the local tangent frame, steering low-bit perturbations toward loss-insensitive axes. Finally, we apply a whitening transformation that maps the Riemannian objective to an equivalent Euclidean form, enabling standard unimodal PTQ methods to evaluate multimodal quantization error under their original assumptions. Across an extensive and diverse set of mainstream VLM benchmarks, RGSQ achieves the highest accuracy and stability under extremely low-bit settings (W2A8 and W3A8). It outperforms VLM-aware baselines, such as MBQ and MQuant, by up to 5.9% and surpasses single-modality improvements by up to 8.6%.

Zhiping Wu, Dongdong Ren, Yangchengyu Zhou +4

State Key Laboratory for Novel Software Technology and the School of Intelligence Science and Technology, Nanjing University, Suzhou Campus, Suzhou 215163, China

VLM Quantization Large Vision-Language Models Post-Training Quantization Low-Bit Quantization

Sep 21, 2026cs.CV

SPHQuant: Efficient extreme low bit weight quantization for Vision-Language Models

Recent foundation models are moving toward native multimodal Vision-Language Models (VLMs), making VLMs a central form of next-generation foundation models. However, their large language backbones make edge deployment difficult due to high memory footprint and memory-bound autoregressive decoding. Weight-only post-training quantization is a practical solution, but pushing VLMs to extreme low bit-widths remains challenging: existing rotation-free methods suffer from outliers at 2-3 bits, while rotation-based methods improve accuracy at the cost of additional runtime overhead. We propose SPHQuant, a rotation-free spherical weight-only quantization framework for VLMs. Instead of quantizing weights directly in Cartesian coordinates, SPHQuant decomposes each 8D weight vector into coordinate signs, radius, and a positive unit direction. This representation isolates outlier magnitude into the radius while keeping directions bounded and statistically regular. Based on this insight, SPHQuant allocates extra precision to the radius to mitigate accuracy degradation induced by outliers. It further uses a compact positive-direction codebook and fine-tunes codebook entries through angular parameterization to preserve the unit-sphere constraint. We also design a hardware-friendly GEMV kernel that keeps the direction codebook small enough for shared-memory lookup and packs radial bits efficiently. Experiments show that SPHQuant matches the performance of state-of-the-art extreme low-bit quantization methods while improving decode throughput over QTIP by 30.3% on RTX A6000. Code will be released in https://github.com/Pushazf/SPHQuant.

Kewei Zhang, Zheng Chen, Haotong Qin +1

Shanghai Jiao Tong University · The Hong Kong Polytechnic University

VLM Quantization Efficient VLM Inference Vector Quantization Weight-Only Quantization Post-Training Quantization Low-Bit Quantization

Sep 17, 2026cs.AR

MiX: Micro-Inverted-Scaling for End-to-End Low-Bit Vision-Language Model Acceleration

The deployment of Vision-Language Models (VLMs) on edge devices is severely bottlenecked by memory bandwidth, necessitating aggressive sub-8-bit quantization. Since edge accelerators are strictly constrained by area and power, they require end-to-end quantized models. However, the extreme dynamic range gap between multi-modal tokens causes standard block formats to suffer "microscaling collapse," where a single massive outlier hijacks the shared exponent, underflowing surrounding elements and destroying attention maps. To break this bottleneck, we propose Micro-Inverted-Scaling (MiX), a novel format that mathematically inverts the microscaling paradigm: rather than grouping multiple mantissas under one shared exponent, MiX groups private, per-element exponents under a single shared mantissa. To handle asymmetric VLM outlier topologies, we introduce an adaptive dual-format (MiX-MX) inference framework. By algebraically factoring out the shared MiX mantissa, this framework maps to a custom accelerator, replacing multipliers with efficient shifters. Evaluated end-to-end on multiple VLMs, our 4.5-bit MiX formulation exhibits equivalent or superior accuracy on multi-modal benchmarks compared to NVFP4. Simultaneously, the MiX accelerator delivers a 25% improvement in area efficiency over the NVFP4 baseline and a 2.3-4.5x speedup with 1.4-2.9x energy reduction across models compared to the state-of-the-art accelerator Focus, proving the inverted-scaling datapath is physically superior for efficient VLM deployment.

Yuan Liao, Jae-sun Seo

Cornell Tech, Cornell University New York, NY, USA

AI Accelerator Inference VLM Quantization Efficient VLM Inference 4-Bit Quantization Low-Bit Quantization

Sep 16, 2026cs.RO

Predict Before You Deploy: Offline Prediction of Quantization-Induced Task Degradation for World Action Models

World action models (WAMs) rely on video-generation backbones, requiring substantial memory and compute for deployment. Post-training quantization reduces memory and can accelerate inference, but bit width, grouping, and quantizer choice define a large configuration space. Identifying configurations that preserve task performance through exhaustive closed-loop evaluation is costly. We propose PreDE (Predict Before You Deploy), a policy-calibrated framework for predicting quantization-induced task degradation from offline action deviations. Using closed-loop outcomes from a small development set, PreDE calibrates two thresholds and accepts, rejects, or defers new configurations using a fixed observation log. Under a within-setting label-ordering hypothesis, the rule issues decisions where all thresholds consistent with the development labels agree. Across five WAMs and four benchmark settings, quantization produces configuration-dependent task losses that cannot be explained by bit width alone or a shared deviation threshold. Across 28 held-out configurations from two policies, PreDE issued 21 decisions before observing closed-loop outcomes (75% coverage), all matching the observed acceptable or degraded labels. Deferred candidates included both acceptable outcomes and a 33-percentage-point loss. In 450 Franka Research 3 trials across two independently fine-tuned policies, all configurations assigned to high-deviation groups before testing showed significant degradation, while low-deviation comparisons showed no statistically significant degradation. On the real robot, W4A4 achieved a 1.37x action-query speedup and approximately 44% lower peak memory. These results support policy-specific behavioral calibration for quantization configuration selection while identifying candidates that require closed-loop evaluation. The code is available at https://github.com/jiuyixu25/PreDE.

Jiuyi Xu, Jinjia Guo, Meida Chen +2

Robotics Program, Colorado School of Mines, Golden, CO USA. · Department of Civil and Coastal Engineering, University of Florida, Gainesville, FL USA. · University of Southern California - Institute for Creative Technology, Los Angeles, CA USA. +1

World Action Models Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Sep 14, 2026cs.CV

VC-Attention: Value Smoothing and Softmax Casting for Low-bit Attention

Diffusion Transformers deliver state-of-the-art video generation, but their long spatiotemporal sequences make attention the dominant deployment cost, and a deployable low-bit kernel must be accurate and fast. Accuracy is limited by outliers: a block's quantization scale is set by its largest entries, leaving typical entries confined to a narrow range of representable values. Prior work smooths queries and keys, but value outliers follow no fixed channel or spatiotemporal structure and remain the dominant source of output error. Speed is limited by softmax: low-bit Tensor Cores accelerate only the two matrix multiplications, so the high-precision exponential between them becomes the longest pipeline stage on datacenter GPUs. We propose VC-Attention, a training-free low-bit attention framework that addresses both by pairing Value smoothing with a fused probability Cast. V-Smooth reorders value tokens by lightweight online clustering, so the tokens in a hardware block quantize well together. It quantizes only the residual after subtracting the block mean, and restores that mean from the row sum the online softmax already maintains. ExpCast-FP8 maps log-domain scores directly to E4M3 probability codes with one fused multiply-add, eliminating the FP32 exponential and the format conversion. We implement VC-Attention for B200, B300, H200, RTX PRO 6000, and RTX 5090. Across Wan2.2, LongCat-Video, HunyuanVideo-1.5, and MiniMax-H3, VC-Attention improves fidelity over low-bit baselines, speeds up the attention kernel over BF16 FlashAttention-4 by 1.46-1.59x on datacenter Blackwell and Hopper and by 2.3-3.6x on workstation cards, and generates a clip 1.13-1.19x and 1.36-1.70x faster end to end.

Xingyang Li, Dongyun Zou, Shining Zhang +8

2MIT · 1Nunchux AI · 3CMU +3

Video Diffusion Models Diffusion Transformer Low-Bit Quantization Diffusion Model Inference Acceleration

Sep 11, 2026cs.CL

Structured Transforms for Low-Overhead Quantization of Language Models

We revisit Kashin-decomposition-based weight quantization for large language models and propose an improved algorithm with stronger convergence properties and structured, efficient orthogonal transforms. The method retains the core factorization of each weight into two components -- one with bounded infinity norm and the other with bounded infinity norm after an orthogonal transformation -- but replaces the dense random orthogonal matrix with a sign-randomized Discrete Cosine Transform (DCT), reducing the per-iteration cost from

\mathcal{O}(N^2)

to

\mathcal{O}(N \log N)

. The proposed greedy algorithm with alternating updates guarantees the four-peak distribution required for stable 2-bit clustering of each factor and admits closed-form initialization of cluster centers, removing the multi-restart k-means bottleneck of prior work. Composed with OPTQ-style sequential error compensation and QuIP-style incoherence preprocessing, the resulting JAX pipeline is competitive with OPTQ, QuIP, QuIP-RG and a fine-tuning- and vector-quantization-free variant of QuIP# at 4-bit per channel on OPT, Llama-2 and Pythia, with favorable wall-clock scaling. The bounded-

\ell_\infty

factorization is also notably robust: on stress configurations where QuIP variants diverge to four-digit perplexity (Pythia-6.9B) or abort with NaNs in LDL back-substitution (Mistral-7B), Kashin-DCT remains numerically stable and stays close to FP16 baseline. At inference time, each weight decomposes into two 2-bit factor codes per channel that are structurally suited to native-2-bit hardware.

Daria Cherniuk, Alexander Rudikov, Boris Kashin +1

Institute of Numerical Mathematics · Steklov Mathematical Institute

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

Sep 9, 2026cs.DB

When Does Low-Bit Quantization Preserve the Decisions of Vector Search?

Low-bit quantization can achieve high recall on some vector representations and fail sharply on others, while average distortion and global rank correlation do not explain the difference. We study quantized vector search at the level of the comparisons consumed by ranking and graph-pruning algorithms. Our first result is a distribution-free decomposition: the probability that a comparison flips is bounded by the probability mass of exact margins near zero plus the tail probability of the calibrated residual. We then account for dependence between residuals that share a query or graph node, and derive covariance-aware second-moment identities and tail bounds under a joint MGF proxy. For a frozen candidate permutation, we prove a deterministic coupling theorem for Vamana neighbour selection: the approximate replay returns the exact neighbour list exactly when all candidate-level pruning actions agree on the frozen exact states. We connect these results to representation geometry through an exact Gaussian oracle, establish a strict correlation gain from a deterministic magnitude bit in an aligned bilinear model, and give a rare-contamination construction showing why marginal Gaussian diagnostics do not imply the required residual tails. When analytical assumptions are unavailable, a held-out block certificate bounds the selective failure risk of a frozen quantized rule. Across learned, classical, and synthetic embeddings, standardized exact margins predict held-out ranking and pruning flip rates substantially better than global rank correlation. The framework applies to coordinate binary codes, RaBitQ, Lucene BBQ, and product quantizers through a common decision interface.

Wenxuan Xiao, Xu Cao

Astrmira Tech.

Vector Quantization Low-Bit Quantization Approximate Nearest Neighbor Search

Sep 9, 2026cs.LG

EFQ-Softmax: Exp-Free Quantization for Softmax

Low-bit attention accelerates Transformer inference by moving the

QK^\top

and

PV

matrix multiplications to FP8 or FP4 matrix engines. However, the softmax path often evaluates shifted-score exponentials in higher precision, forms a temporary probability block, and quantizes it before low-bit

PV

multiplication. This exp-then-quantize path creates a mismatch between a high-precision probability producer and a low-bit matrix consumer. We propose EFQ-Softmax (Exp-Free Quantization for Softmax), a low-bit probability-generation method that directly maps shifted attention scores to block-scaled E2M1 operands. For each microscaling block, EFQ-Softmax selects an exponent-only scale from the local maximum, maps the shifted scores to a normalized residual domain, and generates nonnegative E2M1 probability codes using a single affine rule. The resulting operand is used consistently in both the

\widetilde{P}V

numerator update and the

\widetilde{P}\mathbf{1}

denominator update. The FlashAttention-style row-maximum update, historical rescaling, high-precision accumulation, and final normalization remain unchanged. We evaluate end-to-end quality on Qwen3-8B, Qwen3-VL-8B-Instruct, and WAN2.2-TI2V-5B, and separately measure kernel-level performance on the A5 vector unit. EFQ-Softmax improves the Qwen3-8B seven-task mean from 0.6749 with MXFP4 to 0.6773 and the Qwen3-VL nine-task mean from 0.7826 to 0.8000. On WAN2.2, it maintains temporal consistency and visual quality comparable to the FP16 and MXFP4 baselines under VBench. On the A5 vector unit, EFQ-Softmax reduces the vector-stage latency of the fused probability-generation kernel by 40.33% on average across sequence lengths from 16K to 128K. These results show that direct low-bit probability generation can replace the conventional exp-then-quantize path while preserving end-to-end model quality.

Haohui Han, Yuming Wan, Hongni Wang +4

Xi'an Jiaotong University · Xi’an Jiaotong University · Huawei Technologies Co., Ltd +1

Efficient Transformer Inference Transformer Attention Attention Quantization Low-Bit Quantization

Sep 1, 2026cs.CV

SCULPT: Training Edge Vision Models for Post-Training Quantization Readiness

Edge vision models are difficult to deploy on resource-constrained hardware, making low-bit post-training quantization (PTQ) attractive. In practice, standard FP32 training often produces heavy-tailed activation distributions whose outliers destabilize activation quantization: preserving the full range wastes quantization bins on rare extremes, while aggressive clipping causes information loss. Existing solutions typically rely on quantization-aware training (QAT), which adds training complexity and bit-width coupling, or advanced PTQ procedures that repair the model after training. We present SCULPT (Statistical Clipping and Uniform Loss for Post-Training), a training-time method that improves PTQ readiness during ordinary FP32 fine-tuning. SCULPT combines a topology-aware activation regularizer that suppresses quantization-hostile skewness and kurtosis with a stable percentile-based clipping mechanism that learns deployment-ready activation bounds. Unlike QAT, SCULPT does not simulate quantization during optimization; unlike post hoc outlier-repair PTQ methods, it does not require runtime activation transformations. The learned clipping bounds can be exported directly into a standard PTQ workflow for low-bit deployment, including INT8 and lower-bit settings such as W4A8.

Bharadwaj Kavuri, Sourav Babu-PK, Varadhraj Ellapan +2

Valeo Vision Systems, Tuam, Ireland · Valeo India Pvt. Ltd, Chennai, India

Edge Computing Activation Quantization Post-Training Quantization Low-Bit Quantization

Aug 31, 2026cs.LG

QTEA: Ternary LLMs with Sparse Residual Salient Weight and By-Column Optimization

Weight-only post-training quantization (PTQ) can alleviate the computational burden of serving large language models (LLMs) at scale. However, existing PTQ methods often fail to generalize across models and suffer severe accuracy loss below 2 bits. Many leverage unstructured sparsity to mitigate this loss, but at the cost of regularity and GPU-friendly execution. We present QTEA, a sub-2-bit PTQ framework that quantizes weights into ternary values and uses salient weights as residual error compensators. To maintain hardware efficiency, residuals are assigned to selected columns with semi-structured

1:4

sparsity within the salient columns. We further add column-wise rescale refinement to GPTQ-style column-by-column quantization, alternately updating per-column scales and ternary assignments to reduce reconstruction error. We also identify order-dependent error propagation in GPTQ and introduce error decay to attenuate late-stage error accumulation. On Qwen3-14B, QTEA compresses all weights to an effective 1.7 bits per weight while improving average accuracy over the strongest ternary PTQ baseline by 16.7%. It also achieves 1.40

\times

and 2.61

\times

lower perplexity on WikiText and C4 respectively. This trend holds on Llama3-8B, where QTEA obtains a 6.6% accuracy gain and 1.34

\times

/ 1.95

\times

lower perplexity on the same datasets. Finally, we develop a lookup-table based kernel that achieves 7.2

\times

faster per-token generation over an FP16 baseline. Code is available at https://github.com/Intelligent-Microsystems-Lab/QTEA.

Yipin Guo, Arun M George, Jie Fu +3

University of Notre Dame

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