LLM Quantization

LLM: Large Language Model

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LLM quantization studies how to represent model weights, activations, and attention key-value caches with fewer bits while preserving useful behavior and making deployment more efficient. Post-training methods such as GPTQ and AWQ use calibration data to round weights, while quantization-aware training, mixed-precision allocation, rotations, and outlier handling aim to reduce errors that accumulate across layers. Work also co-designs number formats and GPU, CPU, and edge-device kernels, evaluating trade-offs with language-model perplexity, zero-shot and reasoning benchmarks, memory, latency, and energy. Four-bit inference is often practical, but performance at very low bit widths remains model- and task-dependent, and an open challenge is ensuring that gains in aggregate accuracy do not hide losses in reasoning, safety, fairness, or uncertainty.

Latest papers

388 papers84 papers in the last four weeks, up 121% on the four weeks before. 0.5% of all new papers.

May 22, 2026

Signs Beat Floats: Low-Rank Double-Binary Adaptation for On-Device Fine-Tuning

On-device adaptation of large language models commonly keeps a quantized base model frozen while training and deploying a small, task-specific LoRA adapter. In the unmerged adapter-mode setting, however, the adapter is more than a compact storage module; it introduces an additional dense floating-point branch, maintains a trainable state for local updates, and acts as a unit of communication and hot-swapping.We introduce LoRDBA, a LoRA-compatible adapter that replaces both low-rank factors with binary sign carriers while representing magnitudes through lightweight, channel-wise scales, converting the dense adapter branch into two sign-accumulation matrix multiplications interleaved with channel-wise scaling. A finite-sample analysis shows that reconstruction quality is governed by the residual-to-magnitude ratio of the original LoRA factors. In adapter-mode experiments, LoRDBA outperforms low-bit baselines at matched model sizes while matching fp16 LoRA quality in selected regimes. The unmerged adapter incurs at most 8% prefill latency overhead at matched rank r=16 despite an over 10x reduction in adapter footprint, with moderate training memory overhead of approximately 1.6x that of fp16 LoRA.

Yoshihiko Fujisawa, Yuma Ichikawa, Yudai Fujimoto +2

Fujitsu Limited · Institute of Science Tokyo · RIKEN Center for AIP +1

LLM Quantization Memory-Efficient Fine-Tuning LLM Fine-Tuning Adapter Tuning Low-Rank Adaptation Quantization-Aware LoRA+1

May 21, 2026

GEMQ: Global Expert-Level Mixed-Precision Quantization for MoE LLMs

Mixture-of-Experts Large Language Models (MoE-LLMs) achieve strong performance but incur substantial memory overhead due to massive expert parameters. Mixed-precision quantization mitigates this cost by allocating expert-wise bit-widths based on their importance, approaching the accuracy-memory Pareto frontier and enabling extreme low-bit quantization. However, existing methods rely on layer-wise importance estimation and overlook router shifts induced by quantization, resulting in suboptimal allocation and routing. In this work, we propose Global Expert-level Mixed-precision Quantization (GEMQ) to overcome these limitations via (1) a global linear-programming formulation that captures model-wide expert importance based on quantization error analysis, and (2) efficient router fine-tuning to adapt routing to quantized experts. These components are integrated into a progressive quantization framework that iteratively refines importance estimation and allocation. Experiments demonstrate that GEMQ significantly reduces memory and accelerates inference with minimal accuracy degradation. Source code is available at https://github.com/jndeng/GEMQ .

Jianing Deng, Song Wang, Dongwei Wang +4

University of Pittsburgh · University of Central Florida · University of Arizona +1

Mixed-Precision Quantization LLM Quantization Mixture-of-Experts Language Models LLM Inference Acceleration Mixture-of-Experts Quantization Post-Training Quantization+1

May 19, 2026

Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor

MXFP4 arithmetic can dramatically accelerate reinforcement learning (RL) post-training of large language models (LLMs), yet the quantization error introduces severe accuracy degradation. Existing work treats the quantization error as a monolithic noise term, missing the distinct mechanisms upon interpreting how quantization error damages training. We prove an exact three-way decomposition of quantization error and show how each component dominates a distinct RL training pathway. Our theoretical and empirical analysis decomposes the MXFP4 quantization error into three additive components: "scale bias" from power-of-two rounding, "deadzone truncation" from zeroing small values, and "grid noise" from rounding to the nearest 4-bit grid. Each component dominates a distinct RL failure mode: scale bias accumulates multiplicatively through the backward pass, affecting gradient accuracy; deadzone truncation degrades rollout quality; and grid noise raises the policy's entropy. We combine corrections that are RL failure mode-targeted but not component-exclusive: Macro-block scaling to reduce scale bias, Outlier Fallback recovers deadzone entries, but also partially reduces scale bias induced error, and Adaptive Quantization Noise (AQN) for controlling the policy entropy. On Qwen2.5-3B dense and Qwen3-30B-A3B-Base mixture-of-experts model, the targeted corrections recover BF16 accuracy to within 0.7% and exceed BF16 by +1.0% respectively.

Xiaocan Li, Shiliang Wu, Zheng Shen

Huawei Canada

LLM Quantization 4-Bit Quantization RL Post-Training Post-Training Quantization Neural Network Quantization Quantization Error Compensation

May 19, 2026

Mix-Quant: Quantized Prefilling, Precise Decoding for Agentic LLMs

LLM agents have recently emerged as a powerful paradigm for solving complex tasks through planning, tool use, memory retrieval, and multi-step interaction. However, these agentic workflows often introduce substantial input-side overhead, making the compute-intensive prefilling stage a key bottleneck in long-context, multi-turn inference. In this work, we propose Mix-Quant, a simple and effective phase-aware quantization framework for fast agentic inference. We first investigate FP4 quantization in agentic LLM workflows and observe that quantizing the entire inference process can incur significant performance degradation. In contrast, the prefilling stage exhibits substantial quantization redundancy and can therefore be quantized with minimal accuracy loss, despite being the dominant source of computation. Based on this insight, we apply high-throughput NVFP4 quantization to the prefilling phase while preserving BF16 precision for decoding. By decoupling prefilling acceleration from decoding quality, Mix-Quant combines phase-aware algorithmic quantization with hardware-efficient NVFP4 execution to alleviate the inference bottleneck in LLM agents. Extensive experiments across long-context and agentic benchmarks demonstrate that Mix-Quant largely preserves task performance while delivering significant efficiency improvements, achieving up to a 3x speedup during prefilling.

Haiquan Lu, Zigeng Chen, Gongfan Fang +2

National University of Singapore

LLM Quantization Long-Context Language Model Inference LLM Inference Acceleration

May 19, 2026

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

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

Jinghe Zhang, Daliang Xu, Chenghua Wang +5

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

May 19, 2026

K-Quantization and its Impact on Output Performance

Recent advancements in large language models (LLMs) have shown their remarkable capacities in many NLP tasks. However, their substantial size often presents challenges for deployment. This necessitates efficient techniques for model compression, with quantization emerging as a prominent solution. Despite its benefits, the exact impact of quantization (from 2- to 6-bit) on the performance and accuracy of LLMs remains an active area of research. This paper investigates the performance of eight LLMs at various quantization levels, focusing on tasks such as MMLU-Pro for knowledge processing and reasoning, CRUXEval for code comprehension, and MuSR for reading comprehension. Our results show a consistent trend where higher precision (e.g., 8-bit Q8_0) yields improved performance, albeit with diminishing returns. Aggressive quantization (e.g., 2-bit Q2_K) usually retains acceptable accuracy, though some models show a substantial loss in performance. Our findings indicate that while lower bit precision generally reduces performance, the impact varies across models and tasks. Larger models show greater resilience to aggressive quantization, but can still undergo significant drops at lower precision levels. Mid-sized models in the 7-9 billion parameter range strike an optimal balance between efficiency and resource usage. Such results provide insights into the trade-offs between model size, quantization, and performance.

Robin Baki Davidsson, Pierre Nugues

Lund University · Lund, Sweden

LLM Quantization LLM Evaluation Low-Bit Quantization

May 19, 2026

TORQ: Two-Level Orthogonal Rotation for MXFP4 Quantization

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

Zukang Xu, Xing Hu, Dawei Yang

1Houmo AI.

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

May 18, 2026

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

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

π/(π-2) \approx 2.75

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

p \to 0

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

\cos^2 \to 2/π

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

0.365

) matches the pre-ReLU value

1-2/π

within

0.4\%

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

2.75\times

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

α

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

R \approx nα^2

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

p \leq 0.5\%

), count-matched NLL leverage stabilizes at

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

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

5.0\times

falls within

R_{\mathrm{col}} \leq 19

(

67\times

PPL gap reflects metric nonlinearity). Measured outlier

α

at layer 12 (median

0.024

, max

0.26

) confirms heavy-tailed concentration. The Bussgang constant

2/π

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

R \propto nα^2

accounting for real-model deviations.

Lei Dong

Independent Researcher

LLM Quantization Ternary Quantization Neural Representation Geometry Neural Network Quantization

May 18, 2026

GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets

Mixed-precision quantization improves the budget--accuracy trade-off for large language models (LLMs) by allocating more bits to sensitive modules. However, automating this allocation at LLM scale faces a unique combination of constraints: learnable approaches require quantization-aware training, which is infeasible for billion-parameter models; training-free alternatives rely on static proxy metrics that miss cross-module interactions and must be recomputed per target budget; and search-based methods are expensive without guaranteeing exact budget compliance. We propose GAMMA, a quantizer-agnostic framework that learns module-wise precision preferences entirely within a post-training pipeline. GAMMA optimizes a teacher-forced hidden-state reconstruction objective under an augmented Lagrangian constraint, and projects the learned preferences into exact budget-feasible discrete assignments via integer programming. A key property is score reuse: because the learned preferences encode a stable sensitivity ranking rather than budget-specific weights, a single training run serves arbitrary deployment targets by re-solving only the integer program, reducing per-budget adaptation from hours to a few minutes. Across Llama and Qwen models (8B--32B), GAMMA outperforms both fixed-precision baselines (up to +12.99 Avg.) and search-based mixed-precision methods (up to +7.00 Avg.), and can match fixed 3-bit quality at 2.5-bit average precision, enabling deployment at substantially smaller memory footprints.

Zhangyang Yao, Haiyan Zhao, Haoyu Wang +3

Beihang University · Tsinghua University · ByteDance Inc

Mixed-Precision Quantization LLM Quantization Post-Training Quantization

May 18, 2026

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

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

Le Su, Xing Luo, Zhi Jin

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

LLM Quantization Post-Training Quantization PID Control Low-Bit Quantization Neural Network Quantization Quantization Error Compensation

May 18, 2026

Attention Sinks and Outliers in Attention Residuals

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

Haozheng Luo, Haoran Dai, Shaoyang Zhang +10

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

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

May 17, 2026

WinQ: Accelerating Quantization-Aware Training of Language Models Around Saddle Points

Quantization-aware training (QAT) is widely adopted to quantize language models by training full-precision weights using gradients from the quantized model. The main bottleneck is its slow convergence and early performance plateau, particularly below 4-bit-widths. While this problem has been observed in prior work, its precise cause remains unclear. In this paper, we analyze the convergence of QAT by estimating the spectrum of the loss-surface Hessians. We find that the weights converge to flat regions around saddle points, where a large fraction of the Hessian eigenvalues are both positive and negative. During training, an increasing fraction of Hessian eigenvalues concentrates around zero, whose magnitude decreases. At lower bit-widths, the magnitude of eigenvalues in the Hessian spectrum is significantly smaller. To mitigate these issues, we propose an algorithm called WinQ to accelerate QAT, which involves: (1) periodically resetting weights to the linear interpolation of full-precision and quantized weights, reducing the distance to the quantization grid and increasing eigenvalue magnitude, and (2) computing gradients of noise-injected weights to regularize the Hessian. Extensive experiments show that WinQ accelerates QAT by up to 4 times across various quantization methods and models. Under the same training cost, WinQ improves state-of-the-art sub-4-bit quantization by up to 8.8%. These results are consistent across 16 settings with different language models, quantization methods, and bit widths.

Dongyue Li, Zechun Liu, Kai Yi +6

1Northeastern University, MA · 2Meta AI, CA.

LLM Quantization Quantization-Aware Training Neural Network Optimization Low-Bit Quantization

May 15, 2026

Measuring Maximum Activations in Open Large Language Models

The dynamic range of activations is a first-order constraint for low-bit quantization, activation scaling, and stable LLM inference. Prior work characterized outlier features and massive activations on pre-2024 LLaMA-style models, and the downstream activation-quantization stack inherits that picture without revisiting it for the post-LLaMA open-model boom. We ask the deployment-oriented question: how large can activations get in modern open LLMs, and how does this magnitude vary across families, generations, and training stages? Under a unified pipeline (5,000-sample multi-domain corpus, family-specific tokenization, identical hooks across embeddings, hidden states, attention, MLP/MoE, SwiGLU gates, and final norm), we measure global and layerwise maxima on 27 checkpoints from 8 open families spanning dense, MoE, vision-language, intermediate-training, and instruction-tuned variants. We find that (i) global maxima span over nearly four orders of magnitude at comparable parameter counts, with Qwen3.5 and MoE checkpoints in the 10^2 to 10^3 range and Gemma3-27B-it reaching ~7 x 10^5; (ii) cross-family and cross-generation comparisons break simple monotonic scaling; and (iii) MoE checkpoints exhibit 14.0-23.4x lower peaks than matched-scale dense counterparts, while the residual stream carries the global maximum in 22/24 checkpoints. A lightweight INT-8 sanity check shows that measured maxima co-vary with low-bit reconstruction error via activation-scale selection. We conclude that maximum activation magnitude is a model property tied to family, architecture, and training stage - not a simple byproduct of size - and should be measured and reported alongside any open-weight release before low-bit deployment. The code is publicly available at https://github.com/clx1415926/Max_act_llm.

Luxuan Chen, Han Tian, Xinran Chen +9

1Shanghai Jiao Tong University · 2Baidu Inc. · 4Nankai University +1

LLM Quantization Activation Outliers Activation Quantization Massive Activations

May 14, 2026

Widening the Gap: Exploiting LLM Quantization via Outlier Injection

LLM quantization has become essential for memory-efficient deployment. Recent work has shown that quantization schemes can pose critical security risks: an adversary may release a model that appears benign in full precision but exhibits malicious behavior once quantized by users. However, existing quantization-conditioned attacks have been limited to relatively simple quantization methods, where the attacker can estimate weight regions that remain invariant under the target quantization. Notably, prior attacks have consistently failed to compromise more popular and sophisticated schemes, limiting their practical impact. In this work, we introduce the first quantization-conditioned attack that consistently induces malicious behavior that can be triggered by a broad range of advanced quantization techniques, including AWQ, GPTQ, and GGUF I-quants. Our attack exploits a simple property shared by many modern quantization methods: large outliers can cause other weights to be rounded to zero. Consequently, by injecting outliers into specific weight blocks, an adversary can induce a targeted, predictable weight collapse in the model. This effect can be used to craft seemingly benign full-precision models that exhibit a wide range of malicious behaviors after quantization. Through extensive evaluation across three attack scenarios and LLMs, we show that our attack achieves high success rates against a broad range of quantization methods on which prior attacks fail. Our results demonstrate, for the first time, that the security risks of quantization are not restricted to simpler schemes but are broadly relevant across complex, widely-used quantization methods.

Xiaohua Zhan, Kazuki Egashira, Robin Staab +2

ETH Zurich

LLM Quantization LLM Backdoor Attacks Adversarial Attacks on LLMs Post-Training Quantization

May 14, 2026

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

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

Earl Killian

Mixed-Precision Quantization LLM Quantization Weight-Only Quantization Hardware-Aware Quantization Post-Training Quantization Low-Bit Quantization+1

May 14, 2026

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

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

Thomas Witt

Gemini Stiftung Leipzig

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

May 13, 2026

High-Rate Quantized Matrix Multiplication II

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

Σ_X

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

Σ_X

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

\frac{2πe}{12}

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

Σ_X

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

Or Ordentlich, Yury Polyanskiy

the Hebrew University of Jerusalem, Israel · MIT, USA

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

May 13, 2026

Multi-Scale Dequant: Eliminating Dequantization Bottleneck via Activation Decomposition for Efficient LLM Inference

Quantization is essential for efficient large language model (LLM) inference, yet the dequantization step-converting low-bit weights back to high-precision for matrix multiplication has become a critical bottleneck on modern AI accelerators. On architectures with decoupled compute units (e.g., Ascend NPUs), dequantization operations can consume more cycles than the matrix multiplication itself, leaving the high-throughput tensor cores underutilized. This paper presents Multi-Scale Dequant (MSD), a quantization framework that removes weight/KV dequantization from the GEMM critical path. Instead of lifting low-bit weights to BF16 precision, MSD decomposes high-precision BF16 activations into multiple low-precision components, each of which can be multiplied directly with quantized weights via native hardware-accelerated GEMM. This approach shifts the computational paradigm from precision conversion to multi-scale approximation, avoiding INT8-to-BF16 weight conversion before GEMM. We instantiate MSD for two weight formats and derive tight error bounds for each. For INT8 weights (W4A16), two-pass INT8 decomposition achieves near 16 effective bits. For MXFP4 weights (W4A16), two-pass MXFP4 decomposition yields near 6.6 effective bits with error bound 1/64 per block surpassing single-pass MXFP8(5.24 bits) while maintaining the same effective GEMM compute time. We further derive closed-form latency and HBM traffic models showing that MSD avoids the Vector-Cube pipeline stall caused by dequantization and reduces KV cache HBM traffic by up to 2.5 times in attention. Numerical simulations on matrix multiplication and Flash Attention kernels confirm that MSD does not degrade accuracy compared to dequantization baselines, and in many settings achieves lower L2 error.

Lingchao Zheng, Yuwei Fan, Jun Li +5

Huawei

LLM Quantization LLM Inference Acceleration

May 12, 2026

Grid Games: The Power of Multiple Grids for Quantizing Large Language Models

A major recent advance in quantization is given by microscaled 4-bit formats such as NVFP4 and MXFP4, quantizing values into small groups sharing a scale, assuming a fixed floating-point grid. In this paper, we study the following natural extension: assume that, for each group of values, we are free to select the "better" among two or more 4-bit grids marked by one or more bits in the scale value. We formalize the power-of-two-grids (PO2) problem, and provide theoretical results showing that practical small-group formats such as MXFP or NVFP can benefit significantly from PO2 grids, while the advantage vanishes for very large groups. On the practical side, we instantiate several grid families, including 1) PO2(NF4), which pairs the standard NF4 normal grid with a learned grid, 2) MPO2, a grid pair that is fully learned over real weights and activations, 3) PO2(Split87), an explicit-zero asymmetric grid and 4) SFP4, a TensorCore-implementable triple which pairs NVFP4 with two shifted variants. Results for post-training quantization of standard open models and pre-training of Llama-like models show that adaptive grids consistently improve accuracy vs single-grid FP4 under both weight-only and weight+activation. Source code is available at https://github.com/IST-DASLab/GridGames.

Vage Egiazarian, Erik Schultheis, Andrei Panferov +3

ISTA · Aril Computer · ETH Zürich +1

LLM Quantization 4-Bit Quantization Activation Quantization Post-Training Quantization

May 12, 2026

SOAR: Scale Optimization for Accurate Reconstruction in NVFP4 Quantization

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

Chengzhu Bao, Xianglong Yan, Zhiteng Li +3

Shanghai Jiao Tong University · Tencent Hunyuan

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

May 12, 2026

PRISM: A Geometric Risk Bound for Decomposing Drift into Scale, Shape, and Head

A single base LLM now comes with dozens of post-training variants, quantized, LoRA-adapted, or distilled, and each has to be checked before release. Existing evaluations provide only a partial picture: benchmark scores and likelihood screens say that a variant has degraded, similarity scores such as CKA and SVCCA say how its features moved, and nothing connects the two. We connect them with one structural fact and one design choice: the prediction head is linear, so feature geometry reaches the loss, and we compare the two feature sets through an orthogonal map, which leaves the geometry being measured unchanged. From these we derive PRISM, a closed-form upper bound on the cross-entropy risk gap between a target model and a proxy variant, and prove that it splits exactly into three measurable axes: scale, shape, and head. Each axis names a failure mode and where to intervene: low-bit quantization distorts shape and, at the lowest bit-widths, also inflates activation scale; quantizing the output embedding inflates the head term, which dominates the bound at high bit-widths. Because the shape term is differentiable, the same geometry becomes a regularizer that curbs catastrophic forgetting more than experience replay. Across two model families and five benchmarks, PRISM ranks quantized and fine-tuned variants from a single forward pass at mean Spearman above 0.8, and eight reference sequences already recover the ranking that the risk gap itself needs over a hundred to reach.

Chieh-Yen Lin, Shao-Hua Sun

Appier AI Research · National Taiwan University

LLM Quantization LLM Evaluation LLM Auditing Language Model Robustness

May 12, 2026

Efficient LLM-based Advertising via Model Compression and Parallel Verification

Large language models (LLMs) have shown remarkable potential in advertising scenarios such as ad creative generation and targeted advertising. However, deploying LLMs in real-time advertising systems poses significant challenges due to their high inference latency and computational cost. In this paper, we propose an Efficient Generative Targeting framework that integrates adaptive group quantization, layer-adaptive hierarchical sparsification, and prefix-tree parallel verification to accelerate LLM inference while preserving generation quality. Extensive experiments on two real-world advertising scenarios demonstrate that our framework achieves significant speedup with acceptable quality degradation, making it operationally viable for practical deployments.

Wenxin Dong, Chang Gao, Guanghui Yu +9

Baidu Inc. Beijing, China

LLM Quantization LLM Compression Online Advertising LLM Inference Acceleration

May 11, 2026

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, 2026

Compander-Aligned Query Geometry for Quantized Zeroth-Order Optimization

Low-bit forward evaluation is an attractive route to memory-efficient zeroth-order (ZO) adaptation: the optimizer needs only scalar losses, and the model can be queried near deployment precision. The obstacle is that a quantized ZO query is not a continuous finite difference followed by harmless storage rounding. The query chooses endpoints, the low-precision engine rounds them, and the loss difference is measured along the rounded chord. For nonuniform companding quantizers, this makes the codebook insufficient to predict ZO behavior: a fixed weight-space radius can collapse in dense cells, over-span sparse cells, or assign a rounded chord to an unrounded update direction. We identify the missing object as query geometry and model scalar nonuniform quantization as

Q = φ^{-1} \circ U \circ φ

. CAQ-ZO (Compander-Aligned Queries for Zeroth-Order Optimization) forms one-grid-step Rademacher stencils

z \pm Δr

in

z = φ(x)

, maps endpoints back through

φ^{-1}

, and updates in

z

. Our theory proves the grid-span mismatch, decomposes endpoint-rounding estimator residuals, and gives stationarity bounds in which generic off-grid queries retain a

Δ^2/μ^2

residual channel while CAQ-ZO makes the query-time residual exactly zero. Synthetic experiments isolate this channel, and matched NF4 Qwen/Llama fine-tuning shows that CAQ-ZO improves the trained NF4 baseline under the same quantizer and evaluation budget.

Yao Shu, Zilin Zhu

HKUST-GZ

LLM Quantization Zeroth-Order Optimization Memory-Efficient Optimization Quantization

May 11, 2026

BCJR-QAT: A Differentiable Relaxation of Trellis-Coded Weight Quantization

Trellis-coded quantization sets the current 2-bit post-training frontier for LLMs (QTIP), but pushing below the PTQ ceiling requires quantization-aware training, and QAT on a trellis is obstructed by the non-differentiable Viterbi argmax. We introduce BCJR-QAT, a relaxation that replaces the argmax with the BCJR forward-backward sum-product algorithm at temperature

T

, producing a soft codeword equal to the Boltzmann expectation over trellis paths, exactly differentiable, recovering the hard QTIP code as

T \to 0

, and mathematically identical to the transfer-matrix computation for a 1D Ising-like spin chain. We contribute (i) a fused Triton kernel making BCJR tractable on a single consumer GPU (

6.57\times

speedup, fp32 parity); (ii) a quantitative drift-budget theory of when BCJR-QAT can escape the QTIP-PTQ Voronoi basin, verified across four experiments; and (iii) a positive empirical result on Llama-3.2-1B at 2 bpw under end-to-end forward-KL distillation: with the right schedule (skip the high-

T

phase to avoid an overshoot we diagnose), single-layer BCJR-QAT beats QTIP-PTQ by

\mathbf{-0.084}

PPL on WikiText-2, and multi-layer compounding is super-additive.

Venugopalan Iyengar

LLM Quantization Quantization-Aware Training

May 11, 2026

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 11, 2026

Pretraining large language models with MXFP4 on Native FP4 Hardware

Why does full-pipeline FP4 training of large language models often diverge, even when forward activations and activation gradients remain stable? We address this question through a controlled study of MXFP4 quantization in transformer training, progressively enabling FP4 across forward propagation (Fprop), activation gradients (Dgrad), and weight gradients (Wgrad) while holding all other factors fixed. In full pretraining of Llama 3.1-8B on the C4 dataset, we observe that quantizing Wgrad is the primary driver of convergence degradation, whereas FP4 in Fprop and Dgrad alone introduces only modest additional token requirements. To interpret this behavior, we evaluate both structured and stochastic interventions under a controlled experimental setting. We find that stochastic rounding and randomized Hadamard rotations fail to stabilize training once Wgrad is quantized, whereas deterministic Hadamard rotations consistently restore stable optimization. These results suggest that FP4 training instability is driven by structured micro-scaling errors along sensitive gradient paths, rather than by insufficient stochasticity. We run experiments with native MXFP4 support on AMD Instinct MI355X GPUs, enabling controlled investigation of these effects without reliance on software emulation.

Musa Cim, Poovaiah Palangappa, Miro Hodak +3

1The Pennsylvania State University · 2Advanced Micro Devices, Inc.

Language Model Pretraining LLM Quantization Walsh-Hadamard Transform

May 9, 2026

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 9, 2026

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

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

Euntae Choi, Sumin Song, Sungjoo Yoo

Seoul National University

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

May 9, 2026

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

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

Beshr IslamBouli, David Jin

Massachusetts Institute of Technology, Cambridge, MA, USA.

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