Post-Training Quantization

Also known as PTQ

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Overview

Post-training quantization (PTQ) converts a trained model to lower-precision numbers without retraining it, reducing memory use and enabling inference on constrained hardware. Methods range from rounding and calibration-based scaling to Hessian-aware reconstruction such as GPTQ, rotations and outlier handling, codebooks, and mixed-precision allocation across layers, experts, or caches. Calibration usually uses a small set of representative inputs, while evaluation spans language-model perplexity and reasoning, vision accuracy, multimodal tasks, and real-device latency and memory. The central tension is that moderate precision often retains task quality, while very low bit widths can amplify errors and alter behavior; calibration and hardware-aware kernels help, but accuracy, behavioral fidelity, and deployment speed do not always move together.

Latest papers

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360 papers70 papers in the last four weeks, up 46% on the four weeks before. 0.4% of all new papers.

Sep 29, 2026

Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape

Post-training quantization (PTQ) methods in the GPTQ family minimize a layer-wise reconstruction error on a uniform grid whose scale must be chosen; the common max-based choice degrades sharply at low bit-widths. We study how sensitive this objective is to the scale. For a layer with i.i.d. Gaussian weights and calibration activations of sufficiently large effective rank, we prove that, as the width grows, the normalized round-to-nearest loss converges with high probability, uniformly over all scales, to the mean-squared error of a uniform quantizer applied to a standard Gaussian; we verify the effective-rank condition for wide, randomly initialized MLPs with odd Lipschitz activations and isotropic Gaussian calibration data. The limiting objective has a unique nondegenerate minimizer, whose scale decreases strictly with the number of levels and whose curvature with respect to relative scale errors decays approximately exponentially with the bit-width. GPTQ experiments on five LLMs show the same trend: the scale rule changes perplexity substantially at 2--3 bits and negligibly from 6 bits on, and a local measure of GPTQ scale sensitivity decreases with bit-width in line with the Gaussian curvature. The Gaussian-optimal scale fails on raw weights; after Hadamard incoherence processing it matches the best searched rule at 3 bits and above without any search, but remains clearly worse at 2 bits.

Jonas von Berg, Massimiliano Datres, Carlo Kneißl +1

Ludwig-Maximilians-Universität München Munich Center for Machine Learning (MCML) Konrad Zuse School of Excellence in Reliable AI (DAAD) · University of Tromso, DLR-German Aerospace Center

Post-Training QuantizationNeural Network QuantizationLLM QuantizationQuantization Sensitivity AnalysisLow-Bit Quantization
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Sep 29, 2026

Calibrate the Decisions That Change the Future: On-Policy Post-Training Quantization for Multimodal Large Language Models

Post-training quantization (PTQ) lowers deployment cost for multimodal large language models, but calibration typically reconstructs fixed sequences with local objectives. This overlooks autoregressive feedback: a quantization-induced token change redirects the prefix and changes future states. Yet on-policy coverage alone is insufficient because many decision mismatches barely affect future generation. We propose OnPTQ, an on-policy framework that calibrates on trajectories visited by the current quantized policy. On shared prefixes, OnPTQ identifies quantization-eroded boundaries, evaluates competing tokens through short counterfactual rollouts, and combines current discrepancy with branch consequence into a Decision--Consequence risk. The risk prioritizes critical states, while context anchoring and trajectory refresh preserve multimodal behavior and keep calibration aligned with the updated policy. We further derive a Decision--Consequence bound linking behavioral deviation to current policy discrepancy and action-conditioned future-value span. Across vision--language and omni-modal Qwen models under multiple low-bit settings, OnPTQ improves downstream performance and yields fewer correctness flips against the corresponding Dense/FP16 references, without changing the deployed inference graph.

Wenxiao Fan, Jingling Fu, Lichen Ma +6

School of Computer Science and Technology, Beijing Institute of Technology · Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University

LLM QuantizationVLM QuantizationMultimodal Large Language ModelsPost-Training Quantization
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Sep 29, 2026

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 AccelerationAttention QuantizationKV-Cache QuantizationMulti-Head Latent AttentionPost-Training QuantizationLow-Bit Quantization+1
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Sep 29, 2026

Replay the Curvature: Accurate and Scalable NVFP4 Quantization for Large Language Model Inference

Large language models make weight storage and memory traffic major inference costs, motivating low-precision formats that represent each weight with only a few bits. Such formats use a scale to map floating-point values into a small codebook; NVFP4 improves local range utilization by letting every 16 E2M1 weights share an E4M3 block scale. Choosing that scale is difficult in GPTQ because quantizing one column updates those that follow, so evaluating a block independently can misestimate its final reconstruction error. Large models pose a second challenge: full-precision weights, calibration activations, and second-order state cannot all remain on one accelerator, while assigning complete layers to devices leaves each time-consuming layer solve serial. We introduce Schur Replay, a scale-selection algorithm that reproduces the GPTQ updates caused by each block scale and scores the resulting block error after accounting for compensation from unquantized columns. Separately, our execution infrastructure keeps only the active layer resident, tiers activations across device, host, and disk, retires full-precision layers after export, and distributes independent output rows across tensor-parallel ranks. Together, the algorithm and infrastructure attain 99.35%99.35\% and 100.84%100.84\% question-weighted recovery from BF16 across seven benchmarks on Qwen3.5-397B-A17B and Llama-3.3-70B-Instruct. On the 397B model, the infrastructure reduces measured per-layer time by 15.17×15.17\times over ModelOpt and 23.14×23.14\times over LLM Compressor, with lower memory used per GPU.

Ruiyi Ding, Jie Li, Kang He +4

KlingAI Research · University of Science and Technology of China · Fudan University +2

LLM QuantizationPost-Training Quantization4-Bit Quantization
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Sep 28, 2026

IMC-CLINIC: Coupled Loss-Informed Newton Iterations for Clipping in Analog In-Memory Computing

Analog in-memory computing (IMC) offers a promising path toward energy-efficient large language model (LLM) inference by executing matrix multiplications (MatMul) directly within memory arrays in the analog domain. Its efficiency, however, comes with an additional source of error: limited-precision analog-to-digital converters (ADCs) quantize accumulated analog partial sums, introducing output-side error distinct from conventional activation and weight quantization at the MatMul inputs. Clipping can mitigate both operand and ADC quantization errors, but the optimal clipping factors must jointly balance activation rounding and clipping, weight rounding and clipping, and ADC quantization. Existing clipping methods, designed for digital quantization, do not explicitly optimize these coupled sources of IMC error and often rely on costly search-based calibration. We introduce IMC-CLINIC (Coupled Loss-Informed Newton Iterations for Clipping), a clipping calibration framework based on an analytical surrogate for IMC MatMul output error. The surrogate jointly models operand quantization, accumulated clipping-induced bias, and ADC quantization, enabling efficient evaluation of its gradient and approximate curvature from a small calibration set. IMC-CLINIC jointly optimizes activation and weight clipping factors using a safeguarded Newton-type method. Across multiple models and datasets, it improves average zero-shot accuracy by 6.5-11.5 percentage points over the grid search baseline while reducing calibration time by factors of 10.0-12.1. Its analytical surrogate closely tracks empirical IMC output error, and its optimizer is certified within 1% of the global optimum under the loss objective across all projections on two representative models.

Yung-Chin Chen, Chia-Yu Chen, Naveen Verma

Princeton University, NJ, USA · EnCharge AI, CA, USA

LLM QuantizationCompute-in-MemoryLanguage Model CalibrationPost-Training QuantizationNeural Network Quantization
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Sep 28, 2026

SubRot: Signed Gradient Subspace Calibration for VLM Rotation Quantization

Post-training quantization reduces the deployment cost of vision-language models (VLMs), but preserving multimodal capabilities at low bit widths remains challenging. Existing methods rely on modality- or token-level gradient statistics, which are susceptible to cross-sample variations in visual-to-textual token ratios and the positions of visual information, limiting statistical stability. Moreover, overly coarse aggregation through absolute values and averaging discards gradient signs and channel-wise differences, limiting the separation of modality-specific sensitivities. In contrast, the channel space provides a shared coordinate system across samples, making it a more natural basis for capturing stable task-sensitive structures. We therefore propose SubRot, a signed gradient subspace calibration method for VLM rotation quantization. Through eigendecomposition of the empirical Fisher matrix of activation gradients, SubRot identifies a sensitive channel subspace with three properties: cross-sample stability, clear sensitivity separation, and consistent signed effects on the autoregressive loss along certain directions. Guided by a local Taylor expansion, SubRot combines signed first-order guidance along sign-stable directions with second-order constraints along the remaining sensitive directions, while retaining MSE for overall reconstruction quality. This objective steers quantization errors toward loss-decreasing directions while controlling their magnitude. Experiments on five VLMs across five benchmarks show consistent average-score improvements over FlatQuant under W4A6 and W4A4, reaching 1.4 percentage points on LLaVA-NeXT-7B. Under W4A4, average accuracy degradation from FP16 remains within 1.4 percentage points across all evaluated models, while LLaVA-v1.5-13B exceeds its FP16 average score by 0.4 percentage points.

Zhenhao Shang, Haizhao Jing, Haokui Zhang +4

Northwest Polytechnical University · Nanjing University of Science and Technology · Intellifusion +1

VLM QuantizationRotation-Based QuantizationVLM CalibrationPost-Training Quantization
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Sep 28, 2026

P4Q: Co-designing Token Pruning and Quantization for Vision-Language Model Acceleration

Vision language models have achieved strong performance across a wide range of multimodal applications, yet their substantial computational and memory costs hinder efficient deployment. Visual token pruning and post-training quantization reduce inference overhead along two complementary dimensions, namely sequence length and numerical precision. Existing workflows typically optimize these techniques independently or apply them sequentially. Their distinct optimization objectives leave critical interactions unaddressed and constrain the achievable compression performance. We revisit these designs and present P4Q, a practical co-design framework that jointly optimizes visual token pruning and low-bit quantization for efficient VLM inference. First, P4Q introduces a quantization-aware visual token selection strategy before the LLM. It applies fake quantization to copies of the features produced by the projector and selects visual tokens using statistics computed from these fake-quantized features, thereby conditioning the selector's feature-based decisions on simulated low-bit perturbations. Second, P4Q introduces a pruning-aware quantization calibration strategy. It uses the same selection strategy as pruning to calibrate the quantized model on the retained-token distribution, thereby aligning the calibration process with the pruned execution path used during deployment. By coupling these two components, P4Q achieves substantial inference speedups while maintaining comparable task performance, resulting in a better efficiency-accuracy trade-off than independently optimized pipelines. For instance, on LLaVA-NeXT, P4Q achieves an average end-to-end inference speedup of 2.8x across eight distinct test sets, while retaining higher accuracy than prior compression and quantization methods.

Haizhao Jing, Zhenhao Shang, Haokui Zhang +2

Northwest Polytechnical University · Intellifusion

VLM QuantizationEfficient VLM InferencePost-Training QuantizationVisual Token PruningNeural Network Compression
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Sep 28, 2026

From Attention Sensitivity to Layer Role: Revisiting Mixed-Precision Quantization of Transformers

Most post-training quantization pipelines fit each weight matrix to its pretrained counterpart, one matrix at a time. Whether that proxy tracks what an attention block actually computes, or how errors in the Q, K and V projections compound inside the softmax, is rarely checked. We write the objective on the attention output instead, over all three projections at once, and reuse it throughout the pipeline. JAB defines one scalar loss over the joint Q, K, V weights of a block, evaluated against the block's real causally-masked attention output, and uses it twice: to fit the quantized weights (GPTQ warm start, then STE with learnable scales), and to score the block for a multiple-choice knapsack allocation. On attention-only quantization of Mistral-7B this works. At 3 bits JAB recovers 77-90% of the gap between uniform GPTQ and full precision, and its sensitivity estimate tracks an oracle costing 73 forward passes to within a fraction of a point. It stops working once MLP layers enter the allocation. A role-aware offset rule needing no sensitivity estimate at all beats JAB on GPT-2's MLP and on the full Mistral-7B model: with a 3-bit floor it quantizes 96.4% of the weights to 4.5 bits per parameter at 6.933 perplexity, within 4.4% of full precision (6.643) at 3.56x compression, against 7.158 for JAB at the same budget. Which matrix a weight sits in matters more than any sensitivity estimate we computed. Two things came out sideways. Block-local reconstruction is an unreliable proxy for end-to-end perplexity: one run improved a block's own objective 4.6x while perplexity rose 32x, which is why every allocation here is validated end-to-end. And on attention-only quantization, fine-tuning moved weights farther from their pretrained values while pulling attention outputs closer, with net gains. Post-training seems to recover attention behavior, not weights.

Nafiseh HosseinpourFardi, Negar Alihadi, Mahmoudreza Babaei +2

Sharif University of Technology, Tehran, Iran · GISMA University of Applied Sciences, Potsdam, Germany · BRAINS, Brandenburg Research Center for Applied Intelligent Systems, Potsdam, Germany +3

Mixed-Precision QuantizationLLM QuantizationAttention QuantizationPost-Training QuantizationNeural Network QuantizationQuantization
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Sep 28, 2026

Beyond Reconstruction Loss in Post-Training Quantization: Balanced Fitting for Large Vision-Language Models

Post-training quantization (PTQ) enables efficient deployment of large vision-language models (LVLMs), but is typically calibrated on a small set while expected to generalize across diverse downstream tasks. Although recent PTQ methods for LVLMs incorporate sensitivity signals, they still minimize reconstruction loss with respect to the full-precision model, potentially over-preserving FP behavior and calibration-specific bias. Rather than treating quantization solely as an error to be minimized, we observe that it can also provide beneficial regularization for certain layers and modalities. Motivated by this observation, we propose Balanced Fitting, a quantization effect-based framework that balances precision and regularization beyond reconstruction-based optimization. By measuring layer- and component-wise quantization effects for weights, vision activations, and text activations, Balanced Fitting combines fine-grained fitting for sensitive components with coarser fitting to exploit potential regularization benefits. Experiments on multiple LVLMs show that our method consistently outperforms prior PTQ approaches under both weight-only and weight-activation quantization, while lower reconstruction loss does not reliably translate into better downstream performance. The source code is publicly available at https://github.com/kmc3661/BFQ

Minchan Kang, Kyeonghye Park, Seungyeon Sa +3

Korea Advanced Institute of Science and Technology (KAIST) · Hanbat National University

VLM QuantizationLarge Vision-Language ModelsActivation QuantizationPost-Training Quantization
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Sep 28, 2026

QuantForge: Discovering Residual Decompositions for MXFP4 Post-Training Quantization

Four-bit post-training quantization can reduce the memory demands of large language models, but preserving accuracy under strict MXFP4 W4A4 requires coordinating several design choices. Coordinate transforms change block-encoding errors, which in turn affect the residuals propagated through the network. The useful algorithmic decomposition is therefore not fully known before search. LLM-driven program evolution offers a way to explore these choices, but performance scores alone do not explain which design should change next. We introduce QuantForge, a PTQ discovery system that records competing explanations, selects controls that distinguish them, and checks that successor code implements the resulting conclusions. This residual compilation guides program revisions while retaining useful programs even when their original explanations are rejected. Remeasuring the revised program reveals the next error to address. This process discovers HiRes, a fixed MXFP4 quantizer that shapes coordinates, refines legal code assignments, and recovers errors along attention and MLP paths. Each stage acts on residuals measured after the preceding stage has executed. Across seven tasks, HiRes achieves the lowest seven-model Robust Fit (0.09300) and the lowest quantized Fit-7 at 32B. In matched-budget comparisons of LLM-driven program evolution, each with 240 evaluator calls, QuantForge reaches a held-out transfer target in six of eight runs, compared with three each for textual memory and reflection memory, and one for score-only evolution, despite evaluating fewer new programs. These results show that QuantForge improves the discovery of transferable PTQ algorithms by turning controlled evidence into subsequent program changes.

Qiulin Shang, Zhoutong Wu, Jie Hu +1

Peking University

LLM QuantizationLarge Language Model-Guided Optimization4-Bit QuantizationPost-Training QuantizationNeural Network QuantizationQuantization
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Sep 28, 2026

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 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 QuantizationLow-Bit QuantizationNeural Network Quantization
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Sep 27, 2026

Quantization Error Is Spectrally Flat: A Single Random Probe Is a Calibrated, Data-Free Sensitivity Estimator, with Application to Budget-Targeted Mixed-Precision Quantization

A single random Gaussian probe gives an unbiased estimate of the squared Frobenius norm of a layer's quantization error. The estimator is well-behaved because round-to-nearest error is spectrally flat. Across 1,683 tensors from a 35B MoE and a 9B dense model, effective dimensionality is 0.93 to 0.96 times the i.i.d. noise value of the same shape, and on the MoE the median is unchanged from 2-bit to 8-bit. The probe coefficient of variation is predictable from tensor shape. One probe measures per-tensor sensitivity to within 4 to 7%; twenty probes reach 1.3 to 1.4%.RAM applies the propagated form of this estimator to budget-targeted mixed-precision quantization with no calibration data. Gaussian probes carrying the network's own input statistics score every tensor at six bit-widths. A knapsack solver allocates bits under an exact byte budget, with guardrails against catastrophic 2-bit assignments. One probe pass serves any budget. Isolated and propagated scores rank tensors independently on Qwen3.5-35B-A3B (Spearman -0.01), yet the propagated probe rank-correlates 0.81 to 0.83 with the GPTQ layer objective from real activations, while the isolated estimator is uncorrelated with it. That objective is the wrong allocation target: at matched bytes on Qwen3.8-27B, a block-output probe beats a vendor IQ3_M mix and an oracle that allocates from the real-activation objective. On Qwen3-8B the propagated probe ties HAWQ-V2 at matched bytes. Across seven architectures from 8B to 122B, with probe timing up to a 400B model in nine minutes on one workstation, RAM reaches 3.5 to 13.6% lower median WikiText-2 perplexity than size-comparable uniform 4-bit builds on the tested MoE models. (Black Sheep Ai baa.ai)

I Kennedy, T Kennedy

baa.ai Auckland, New Zealand

Mixed-Precision QuantizationLLM QuantizationQuantization Sensitivity AnalysisPost-Training QuantizationNeural Network Quantization
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Sep 27, 2026

Chameleon: Dynamic Format Adapter for Efficient Diffusion

Post-training quantization (PTQ) is the standard way to run modern diffusion models on memory-constrained accelerators, yet every existing diffusion PTQ scheme fixes the number format\mathit{number\ format} in advance and only tunes the scale, zero point, or per-layer bit-width. At a fixed bit-width the best format depends on the distribution being encoded, and that distribution differs across weight channels, across layers, and along the diffusion timestep, where activation distributions slide from heavy-tailed and noise-dominated to tightly clustered and structured. We propose Chameleon, a PTQ framework that holds the bit-width fixed and treats the format itself as a discrete variable, chosen per weight channel and per (layer, timestep bucket) activation tensor. Activation formats come from {INT8, FP8 E4M3, FP8 E5M2, MXFP8, MXINT8}, selected ahead of time from two cheap statistics (empirical kurtosis and the closed-form diffusion SNR) and stored in a lookup table; weight formats come from {INT8, MXINT8} at 8 bits or {INT4, NF4, FP4 E2M1, MXINT4, MXFP4} at 4 bits, selected offline by reconstruction error. An architectural fork adapts the same selection layer to multi-step UNets, single-step distilled models, and Diffusion Transformers. Across SDXL, SDXL-Turbo, and PixArt-αα on COCO-2014, Chameleon achieves the best FID in all six backbone ×\times bit-width settings, with CLIP within 0.24 of the FP16 reference and the best of all quantized methods at W4A8W_{4}A_{8}.

Arnab Sanyal, Sandeep Chinchali

UT SWARM Lab, Department of Electrical & Computer Engineering The University of Texas, Austin TX 78712

Diffusion Model QuantizationPost-Training QuantizationDiffusion Model Inference AccelerationNeural Network Quantization
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Sep 27, 2026

PulseQuant: Propagation-Guided Subspace Correction for 4-Bit Video Diffusion Transformers

Quantization errors in video diffusion transformers can be amplified or attenuated by subsequent denoising updates, making local reconstruction error an incomplete predictor of final impact. We introduce PulseQuant, a 4-bit post-training quantization method that combines trajectory sensitivity with activation geometry to guide offline calibration. Isolated block--step interventions estimate propagation risk, which prioritizes sensitive trajectory states during row-radius selection. With these radii fixed, response-subspace correction uses neighboring-code edits to reduce residual components along dominant activation directions. Both stages preserve the original 4-bit weight representation. Controlled interventions show that short-horizon propagated error predicts final latent error more reliably than immediate block-output error, supporting calibration beyond local reconstruction objectives. Evaluations on Wan models, Self Forcing, and MiniMax-H3 demonstrate improvements in key consistency and dense-reference metrics while remaining competitive on other attributes across model scales and generation paradigms.

Yutong Wang, Xingtong Ge, Enhuai Liu +4

The University of Sydney · The Hong Kong University of Science and Technology · The Chinese University of Hong Kong +1

Video Diffusion ModelsDiffusion TransformerDiffusion Model Quantization4-Bit QuantizationPost-Training QuantizationNeural Network Quantization+3
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Sep 27, 2026

Q-WAM: 4-Bit Quantization of World Action Models with Action-Subspace Protection

World Action Models (WAMs) jointly generate video and robot actions through iterative diffusion and perform strongly in robotic manipulation. However, their prohibitive compute and memory costs pose substantial deployment challenges. Post-training quantization (PTQ) can reduce these costs, but existing PTQ methods such as smoothing and rotation are insufficient to maintain the precision of action generation. To overcome this limitation, we propose Q-WAM, a new 4-bit weight-activation quantization for WAMs that preserves the actions the model generates. Specifically, we introduce the Action Observability Gramian (AOG), which measures how much rounding errors in each weighted combination of a layer's input channels change the final action through all denoising steps. We also develop Action-Subspace Protection (ASP), which keeps the few most action-sensitive channel combinations in a tiny 16-bit low-rank branch and quantizes the complementary weights and activations to 4 bits, both as dense matrix multiplications that run efficiently on GPUs. Finally, to preserve action quality with minimal overhead, we identify the experts that matter most for the generated action by aggregating the AOG-derived action mass across the layers of each expert and apply ASP only to those experts. We evaluate Q-WAM on three WAMs, both in simulation and in real-world deployment. On the RoboTwin 2.0 benchmark, it reaches 89.6--93.0% average success rate, within 1.1 percentage points of the 16-bit models, while reducing the memory of the quantized blocks by 3.1--3.4×\times. Our method outperforms the strongest baseline, SVDQuant, by 2.5--8.7 percentage points. On a Unitree G1 humanoid and a bimanual UR3 robot, it improves success over SVDQuant by 12.8-17.6 percentage points.

Arash Akbari, Arman Akbari, Jingwu Luo +7

Northeastern University · EmbodyX · University of Minnesota - Twin Cities +1

Mixed-Precision Quantization4-Bit QuantizationRobotic ManipulationActivation QuantizationPost-Training Quantization
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Sep 26, 2026

PrismQuant: Optimal Null-Space Rotations for Grouped Quantizers

Smaller activation outliers do not necessarily imply better low-bit quantization: their alignment with the quantizer matters. We introduce PrismQuant, a quantizer-aware rotation framework that aligns the leading activation eigenspace with the constant group subspace of asymmetric grouped INT4. The affine offsets represent the energy in this subspace without widening the range within the group. We formulate rotation design as a Ky Fan trace maximization and derive a closed-form solution that is provably optimal for this alignment objective. Compact Householder transformations and their compact-WY representation enable gradient-free construction and efficient application at both foldable and online sites. A predictive range law further connects unaligned activation energy and group size to quantization-relevant variation. Experiments on Llama, Qwen, and Mistral span dense models up to 70B parameters and a 30B mixture-of-experts model. Under W4A4KV4, PrismQuant sets the state of the art on Llama-3.2-3B among the compared methods in both perplexity and accuracy. On Llama-3.1-70B, it attains 3.85 perplexity and 72.46% average zero-shot accuracy, only 0.22 percentage points below full precision. In the deployment study on Llama-3.1-8B, our optimized implementation achieves 1.51x prefill and 1.22x CUDA Graph decode speedups over matched FP16 baselines, with 56.34% lower decode peak memory and only 2.35% additional Graph decode latency over Hadamard. Code and models are available at https://github.com/ForeverBlue816/PrismQuant and https://huggingface.co/collections/ForeverBlue/prsimquant.

Yanlong Chen, Yining Chen, Song Zhang +2

Nanyang Technological University, Singapore · Nanjing University of Posts and Telecommunications, Nanjing, China · Nanjing University, Nanjing, China +1

LLM QuantizationRotation-Based QuantizationActivation Quantization4-Bit QuantizationPost-Training Quantization
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Sep 25, 2026

Depth Laws for the Precision Floor of Trained Neural Networks: Amplification, Residual Scaling, and a Quantization-Aware Training Paradox

How many bits does a network need before its accuracy collapses, and how does this grow with depth? We study the precision floor, the perturbation level or bit-width at which accuracy falls halfway to chance, in MLPs, CNNs, Vision Transformers and nine pretrained language models, under post-training quantization (PTQ) and quantization- or noise-aware training (QAT). (i) A first-order theory sets the floor through one full-precision quantity, the predictive amplification GG: ηc=Λ/Gη_c=Λ/G, and G2G^2 grows linearly in depth at a rate proportional to the squared residual branch scale. (ii) The predicted equality αPTQ=ρα_{PTQ}=ρ of depth exponents holds within 95% intervals in twelve of thirteen trained architectures and in GPT-2 from 12 to 48 layers, with Λ=1.45±14%Λ=1.45\pm14\% across trained architectures. (iii) Residual branches scaled by 1/D1/\sqrt{D} and pre-normalisation remove the depth penalty, and each quantizer turns noise into bits at a rate fixed by its step rule, giving bc=(α/γ)log⁡2D+Cb_c=(α/γ)\log_2 D+C. (iv) A QAT paradox: noise-aware training roughly doubles the tolerable noise of shallow networks, but the gain decays with depth, so the depth law steepens (αQAT/αPTQ=1.45α_{QAT}/α_{PTQ}=1.45-1.471.47 on two datasets, ten seeds each). Decision margins, cross-layer error cancellation and heavy tails do not set the floor.

Ahmad S. Tarawneh

Faculty of Information Technology Mutah University Al-Karak, Jordan

Neural Network QuantizationPost-Training QuantizationQuantization-Aware Training
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Sep 25, 2026

Generalization behavior of OPTQ and the role of regularization

Large neural networks can be compressed by rounding or "quantizing" their weights to numbers that admit representations with fewer bits. One algorithm for quantization, OPTQ, progressively quantizes the weights of a neural network so that the squared quantization error on a specified calibration dataset is as small as possible. We study the performance of OPTQ and a variant algorithm, stochastic OPTQ, in a generalization setting and derive bounds for the expected squared error accrued by the algorithm when a test point is drawn from a fixed distribution. We prove two results. One result relates the generalization error to the error on a calibration dataset comprising independent samples from the same distribution as the test distribution. The other result bounds the generalization error of stochastic OPTQ for all sufficiently nice distributions, regardless of the calibration dataset. In both of these results, the regularization term λλ plays an important role. We use insights from these results to make a new recommendation for the choice of λλ and see that this choice of λλ preforms favorably in experiments when compared to prior recommendations in the literature.

Erin George, Rayan Saab

Neural Network QuantizationPost-Training QuantizationGeneralization BoundsNeural Network Generalization
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Sep 25, 2026

Softmax Reparameterization for Output-Head Quantization

Large vocabularies make output heads a substantial inference cost in small language models. We introduce softmax reparameterization, a post-training method that searches over functionally equivalent output heads before quantization. The method subtracts a scalar multiple of the vocabulary-row mean from every output row and selects the coefficient by validation KL. For linear-softmax heads, these shifts preserve full-precision predictions exactly and require no decoder retraining; a rank-one correction extends the construction to nonlinear logit paths. Across seven output heads and three quantizers, W4 gains are largest where baseline quantization substantially distorts predictions: test KL falls by 93% on XGLM under RTN and by 73--77% on Phi, BLOOM, and BLOOMZ under activation-weighted MSE. Heads with low baseline error change little; at W2, used as a compression stress test, benefits extend more broadly. On Phi, the gains persist under stronger GPTQ calibration; a separate untouched holdout reproduces the improvements on Phi and BLOOM. Frozen WikiText-selected coefficients also transfer without retuning to C4 and OpenWebMath. Residual analysis on Phi shows how fidelity can improve despite greater total logit error: the selected representative reduces error on likely outputs and lowers its Fisher-weighted cost. For shift-compatible heads, the shift adds no inference operation. With the decoder held in BF16, a packed W4 Phi output head reduces batch-one generation latency by 10.8%, and reparameterization preserves this speedup.

Asim Kadav, Christian Flores, Chirag Arora +5

Adobe Search, Discovery & ContentAI

LLM QuantizationPost-Training Quantization
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Sep 25, 2026

Teacher-Anchored Selection of Post-Training Quantized Models under Domain Shift

Compressing a trained model yields a family of deployment candidates, and under domain shift the most compressed one need not be the one to deploy. We study selection over such a family, with candidates and teacher fixed and target labels absent or scarce. Two findings organize the label-free case. Minimum teacher distortion behaves almost as a constant rule, selecting the same eight-bit, per-channel, unclipped configuration in every run, which does not minimize empirical target cross-entropy. Established estimators divide sharply: in the overconfident-collapse regime of the CNN families, confidence-based estimators order the family close to backwards, and the diagnostics that identify it need the labels the setting denies, while output-distribution estimators match the teacher-relative anchor and on one architecture beat it. Distortion is nonetheless stable, so a supervised term can move selection away from it. Combining the two, we give exact quadratic identities for a canonical quadratic analogue of the family. We also show that under symmetric corruption the label-dependent part of a criterion linear in the label indicator is multiplied by one common factor whenever its coefficient sums are candidate-invariant, a class holding teacher contrasts and accuracy but not cross-entropy. These characterize the score's components without bounding selection regret. Across one hundred and thirty-four candidate families, one per independently trained convolutional or Vision Transformer teacher, anchoring reduces mean regret at the smallest label budget in every setting, an advantage that fades beyond twenty-five labels.

Alejandro Rodriguez Dominguez, Muhammad Shahzad, Xia Hong

Department of Computer Science, University of Reading, Reading, United Kingdom · Quantitative Analysis and Artificial Intelligence Department, Miralta Finance Bank S.A., Madrid, Spain · Lecturer, Albert School, Madrid, Spain

Model SelectionPost-Training QuantizationDistribution Shift
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Sep 25, 2026

G2^2PTQ: Improving LLM Post-Training Quantization with Generalized Gradient Compensation

Post-training quantization (PTQ) is a practical approach to reducing the memory and computational footprint of large language models (LLMs) without retraining. GPTQ-based methods have become the de facto standard, yet they suffer from two complementary limitations. Methods with local, layer-wise objectives lack global supervision; while methods with global objectives fix their Hessian estimates at the start and ignore first-order gradients, so their guidance grows stale as quantization proceeds. This paper presents G2^2PTQ, a unified PTQ framework with Generalized Gradient Compensation that integrates both first- and second-order information under a globally supervised, block-wise optimization objective. By refreshing gradient and Hessian estimates before quantizing each Transformer block, G2^2PTQ avoids the staleness of prior global methods. Furthermore, to stabilize the exact first-order compensation, we introduce a trust-region scaling mechanism that dynamically bounds the gradient step to prevent exploding weight updates. Finally, we derive efficient implementations for block-wise Hessian approximation and exact gradient compensation. Experimental results on various model families and bit-widths demonstrate that G2^2PTQ enables better alignment with the full-precision model, outperforming state-of-the-art baselines. Code is available at: https://github.com/G2PTQ/G2PTQ.

Ruikang Liu, Haoli Bai, Yuxuan Sun +8

ZTE Corporation · The Chinese University of Hong Kong · Northwestern Polytechnical University +2

LLM QuantizationPost-Training QuantizationLow-Bit Quantization
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Sep 25, 2026

Low-Bit Recurrent States in Hybrid Language Models

Hybrid language models maintain fixed-size recurrent states, but existing quantizers typically use eight bits or more. Quantization errors persist according to channel decay rates. We derive distortion weights from the observability Gramian and combine them with normalized state ranges for mixed-precision bit allocation, without calibration data, rotation, or training. We also quantize decay rates logarithmically. With per-token state quantization, a four-bit mean payload reduces excess negative log-likelihood by factors of 3.3--27.9 relative to the best of seven baselines across three hybrid models; metadata costs vary. At six bits, negative log-likelihood differs from the FP32-state baseline by less than 0.005 nats. Ablations separate gains from variable bit widths, decay weighting, and range normalization. With less frequent write-backs, gains diminish and depend on the model and budget.

Hongren Chen, Jiayang He

Hybrid Language ModelsRecurrent-State QuantizationLanguage ModelingLow-Bit QuantizationNeural Network QuantizationMixed-Precision Quantization+1
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Sep 25, 2026

Quantizing Looped Transformers: Feedback Exposure and Calibration Blindness

Looped transformers reuse weights across recurrence steps, making low-bit quantization especially attractive. We identify two distinct failure modes of standard post-training quantization. On Huginn-3.5B, per-channel INT4 fails primarily at the non-residual loop-entry adapter, while quantizing the residual core is much less damaging. We call this feedback exposure: a quantized layer perturbs the recurrent state without an identity path, and the resulting error is fed back at later steps. Controlled experiments on linear filters and Mamba state-space models show that feedback exposure also occurs outside transformers. Grouped INT4 reveals a separate failure, calibration blindness: our one-step GPTQ baseline builds its Hessian from step-0 activations, leaving input directions used later in the recurrence nearly unweighted. Across nine checkpoints from seven looped architectures, one-step GPTQ is worse than round-to-nearest (RTN) on the primary task metric for five checkpoints. Accumulating the GPTQ Hessian across recurrence steps outperforms both one-step GPTQ and RTN on all nine checkpoints and recovers bf16-level accuracy on Huginn. These results separate two questions for PTQ on looped models: where quantization error enters the recurrence, and which states calibration sees.

Nux Li

Meta

LLM QuantizationPost-Training QuantizationLow-Bit QuantizationRecurrent Transformers
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Sep 24, 2026

AERIAL: Adversarial Evaluation of Robustness in Accuracy-Preserving Low-Precision EEG Decoders

Deployment-oriented compression is attractive for resource-constrained brain--computer interfaces (BCIs), but whether it changes adversarial vulnerability remains unclear. On BCI Competition IV-2a, we compare 32-bit floating-point (FP32) EEGNet and ShallowConvNet models with global magnitude pruning and simulated INT8 post training quantization (PTQ) and quantization-aware training (QAT) across nine subjects and three seeds. Simulation provides differentiable quantize--dequantize models for white-box attacks and gradient analysis, while native TensorRT deployment is used for validation. Accuracy-preserving compression does not improve direct robustness: at ε=0.005ε=0.005, EEGNet PGD accuracy remains 22--24% across FP32, 50% pruning (P50), PTQ, and QAT. However, P50 reduces bidirectional transfer efficiency to 0.963/0.928 (FP32→\rightarrowP50/P50→\rightarrowFP32), versus 0.994/0.997 for PTQ; the same trend holds for ShallowConvNet. Gradient alignment shows a corresponding separation, while native PTQ agrees with simulated clean/adversarial predictions in 95--98% of cases. These results show that direct robustness, adversarial transfer, and deployment efficiency are distinct properties of compressed EEG decoders.

Saim Rehman, Muhammad Shafique

eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE

Quantization-Aware TrainingEEG DecodingAdversarial RobustnessPost-Training QuantizationAdversarial TransferabilityNeural Network Pruning
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Sep 24, 2026

GHOST-Q: Towards Studying Grounding Hallucinations Overlooked Under Same-score TradeOffs in Quantized VLMS

Post-training quantization of vision--language models (VLMs) is typically assessed through aggregate task accuracy and memory savings, but preserving a headline score does not guarantee preservation of visual grounding behavior. We present GHOST-Q, a cross-precision controlled evaluation of three 8B VLM families under FP16, INT8, and NF4 across utility and hallucination-sensitive benchmarks. Rather than comparing only aggregate accuracy, we pair FP16 and quantized predictions item by-item to quantify how compression redistributes grounding successes and failures. Five of six quantized variants preserve MMStar accuracy within ±2\pm2 percentage points, yet 10 of 36 paired effects remain significant after false-discovery-rate correction, nine on hallucination-sensitive conditions. Same-device A100 profiling further demonstrates that substantial memory reduction does not necessarily mean lower inference latency. Finally, an open-ended AMBER audit reveals strong generation budget censoring whose severity varies by architecture and precision. These results show that quantized VLMs should be evaluated jointly for aggregate utility, grounding reliability, generation behavior, and realized deployment efficiency.

Saim Rehman, Muhammad Shafique

eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE

VLM EvaluationVLM QuantizationVision-Language GroundingPost-Training Quantization
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Sep 24, 2026

Same Bit Width, Different Outcomes: Post-Training Quantization of Text-to-Speech Across Architectures

Post-training quantization (PTQ) reduces the cost of on-device text-to-speech (TTS), but published evaluations cover one system or method. We evaluate PTQ across TTS architectures under one protocol with three core models, weight and activation ablations of eight more, and two held-out models quantized blind. Four-bit per-channel weights reduce UTMOS, a predicted mean opinion score, by 2.8 on Supertonic and 0.07 on Kokoro, and per-tensor scaling can cause severe degradation even at 8 bits. The same bit width yields different outcomes, because the sensitive component is model-specific and not reliably predicted from the model class. A staged ablation procedure identifies it, and per-layer GPTQ can restore it to within 0.1 UTMOS. Real int8 and int4 kernels reproduce the simulated ordering at hardware-dependent cost. On a Mac mini, a 4-bit weight kernel runs Supertonic at 0.60x the fp32 latency while int8 is slower, so each configuration requires validation on the target runtime.

Se Un Park, Yutae Kim, Junyoung Park

UX Factory, Inc.

TTS EvaluationWeight-Only QuantizationActivation QuantizationPost-Training Quantization
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Sep 23, 2026

Temporal Taxation Compounds Under Post-Training Compression of Whisper Models

Automatic speech recognition models are audited for demographic fairness at full precision, yet the models that ship to production have been quantized, pruned, and distilled. We ask whether post-training weight compression, which alters model weights rather than the audio signal or its feature representation, redistributes error burden across demographic groups. Across the Whisper family on Fair-Speech, Common Voice 25, and AfriSpeech-200, 50% Wanda pruning of Whisper-large-v3 sharply widens the Black/AA-vs-Asian temporal-taxation differential on Fair-Speech: the absolute word-error-rate gap between the worst- and best-served groups more than doubles; at an assumed cost of five seconds of correction effort per transcription error this is a rise from 30 to 64 seconds of correction time per minute of speech. This +111% relative increase is invariant to the assumed per-error cost, survives an audio-quality control, and is only partly mitigated by beam-search decoding, which still leaves an +86% increase. At edge model size, INT4 HQQ quantization compounds catastrophic transcript loops on West African accents by factors of five to seven. Distillation, by contrast, narrows demographic gaps in 21 of 27 evaluated settings (teacher-student pair, precision, and dataset), with the exceptions concentrated on a single model pair. We cast the temporal-taxation construct of Choi and Choi (2025) as a quantitative metric, and show that single-snapshot fairness audits on full-precision models do not capture the deployment-time burden that compression places on already-marginalized speakers.

Srishti Ginjala, Eric Fosler-Lussier, Christopher W. Myers +1

The Ohio State University, Columbus, OH, USA · Air Force Research Laboratory, USA

ASR EvaluationSpeech Foundation ModelsDemographic Bias in ASRAutomatic Speech RecognitionPost-Training Quantization
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Sep 23, 2026

Predicting Quantization Price for Selecting PTQ Configurations Before Deployment

Weight-space post-training quantization (PTQ) must choose finite formats, granularities, quantizer families, transformations, and bits before the completed quantized model reveals its output-distribution drift. Existing PTQ methods predict important pieces of this degradation, including reconstruction error, Hessian sensitivity, transformation effects, and downstream loss, but these pieces are usually scored after fixing the quantization geometry or inside separate configuration families. We formulate weight-space PTQ as pre-deployment configuration selection using priced layer-output error. Each admissible layer configuration is treated as an error generator with a deployment cost, which induces a layer-output error covariance Σl(αl)\boldsymbolΣ_l(α_l), and the full-precision model prices that covariance by downstream curvature, ρ^l(αl)=12Tr⁡(H^l Σ^l(αl))\widehatρ_l(α_l)=\frac{1}{2}\operatorname{Tr}\left(\widehat{\mathbf{H}}_l\,\widehat{\boldsymbolΣ}_l(α_l)\right). The price follows from full-precision-to-quantized forward KL, whose first-order term cancels at the reference model. It turns reconstruction and diagonal scores into reduced proxies that drop price factors, while finite formats, codebooks, granularities, and equivalent transformations become comparable candidates through the covariances they induce and the costs they pay. A trace reduction then yields a calibration-time price table and a budgeted price-guided selector, making fixed-geometry bit allocation a special case rather than the organizing problem.

Junbin Qiu, Jian Mu, Weitong Zhang +1

Post-Training QuantizationNeural Network Quantization
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Sep 22, 2026

Disaggregated Quantization: Specializing LLM Prefill and Decode

Prefill and decode reward different approaches to quantization: low-precision arithmetic accelerates prompt processing, while compact weights reduce memory traffic during generation. We propose "disaggregated quantization" (DQ), which specializes computation formats, weights and storage placement to both of these phases. On Qwen 3 and Gemma 3, removing activation quantization specifically on decode improves accuracy on decode-heavy tasks without increasing inference cost. Training separate compute-native prefill weights accelerates prompt processing relative to weight-only inference while matching or exceeding its accuracy at 2-3-bit decode on both decode-heavy and prefill-heavy tasks. With released Qwen3.8-27B GGUF decoders, training an NVFP4 prefiller improves 1-bit accuracy by 32.5 points on MMLU-Pro and 35.3 on MMMU-Pro without modifying the decode checkpoint. To accommodate the additional checkpoint on a single device, offloaded disaggregated prefill (ODP) streams its weights from SSD, amortizing loading over prompt length. On the same 27B model, ODP delivers a 1.78x time-to-first-token speedup over the weight-only baseline at 8K prompt length in llama.cpp. We evaluate accuracy under disaggregated serving in vLLM and further validate shared-weight format disaggregation through post-training quantization on models up to 2.8T parameters.

Andrei Panferov, Maximilian Kleinegger, Sweta Priyadarshi +2

NVIDIA · ISTA

LLM QuantizationLLM InferenceLLM Inference AccelerationPost-Training QuantizationNeural Network QuantizationPrefill-Decode Disaggregation
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Sep 21, 2026

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 QuantizationLarge Vision-Language ModelsPost-Training QuantizationLow-Bit Quantization
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