MGVQ: Synergizing Multi-dimensional Sensitivity-Aware and Gradient-Hessian Fusion for Vector Quantization

Dawei Yang; Xing Hu; Zhong Wang; Zukang Xu

arxiv: 2605.24019 · v1 · pith:UVK4UYBInew · submitted 2026-05-20 · 💻 cs.CV · cs.LG

MGVQ: Synergizing Multi-dimensional Sensitivity-Aware and Gradient-Hessian Fusion for Vector Quantization

Zhong Wang , Zukang Xu , Xing Hu , Dawei Yang This is my paper

Pith reviewed 2026-06-30 17:33 UTC · model grok-4.3

classification 💻 cs.CV cs.LG

keywords vector quantizationvision language modelspost-training quantizationmixed precisionsensitivity analysisgradient hessian fusionmodel compressionultra low bit

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The pith

MGVQ achieves up to 4.9 point accuracy gains in 2-bit quantization of vision-language models by fusing multi-dimensional sensitivity analysis with gradient-Hessian error compensation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Large vision-language models face deployment challenges due to their size, and vector quantization offers a way to compress them to ultra-low bits but must handle differences between visual and textual weights. The paper introduces MGVQ which uses sensitivity-guided mixed-precision to assign bits based on channel importance from global and local views, and incorporates first-order gradients into second-order compensation with efficient matrix decompositions. This approach is shown to outperform previous methods on several VLMs at 2 bits. A sympathetic reader would care because it could make these powerful models runnable on devices with limited memory and compute without losing much performance.

Core claim

The central claim is that integrating multi-dimensional sensitivity perception and gradient-Hessian fusion in MGVQ allows for effective vector quantization of VLMs, overcoming limitations of unified codebooks and ignoring gradient info, resulting in superior performance in 2-bit settings with a maximum accuracy improvement of 4.9 points on InternVL2-26B compared to existing post-training quantization methods.

What carries the argument

The sensitivity-guided structured mixed-precision quantization module that dynamically assigns bit-widths using combined global and local sensitivity analysis, and the gradient-aware second-order error compensation module that embeds first-order gradients and uses Kronecker and Block-LDL decomposition for computational efficiency.

If this is right

VLMs can be quantized to 2 bits with higher accuracy than previous methods, facilitating edge deployment.
The framework applies across mainstream VLMs like LLaVA-onevision, InternVL2, and Qwen2-VL.
Error compensation becomes less biased by including gradient information, reducing deviation from pre-trained states.
Resource allocation is refined by accounting for cross-modality weight distribution differences.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the sensitivity analysis generalizes, MGVQ could be adapted for quantizing other large multimodal models.
The method might inspire similar fusion techniques in other model compression domains like pruning or knowledge distillation.
Testing on even lower bits or different hardware could reveal further benefits or limitations not covered in the experiments.

Load-bearing premise

The load-bearing premise is that multi-dimensional sensitivity analysis combined with embedding first-order gradients into second-order compensation produces bit assignments and error corrections that generalize to new VLMs without dataset-specific tuning.

What would settle it

Running MGVQ on a vision-language model outside the tested set, such as a different architecture or size, and checking if the accuracy at 2-bit quantization still exceeds the best baseline by at least 3 points.

Figures

Figures reproduced from arXiv: 2605.24019 by Dawei Yang, Xing Hu, Zhong Wang, Zukang Xu.

**Figure 1.** Figure 1: Comparison of average accuracy between MGVQ and other quantization methods across different VLMs LDL decompositions. We validate MGVQ across leading VLMs, such as LLaVA-onevision, InternVL2, and Qwen2-VL. Under 2-bit quantization, our method consistently outperforms state-of-the-art PTQ baselines, delivering accuracy gains of up to +4.9 (71.4% vs. 67.0% on InternVL2-26B). These results highlight MGVQ as… view at source ↗

**Figure 2.** Figure 2: Similarity between tokens. (a) Text tokens similarity. (b) Image tokens similarity memory bandwidth, making it a key technique for compressing LLMs(Frantar et al., 2022; Li et al., 2025b; Xu et al., 2025). Currently, PTQ methods can be broadly categorized into two classes. Scalar quantization (SQ), which performs well at medium to high bit-widths (≥ 4 bits), assigns each weight an independent scaling fa… view at source ↗

**Figure 4.** Figure 4: Gradient value at the 99% quantile of the gradient statistics of the 31st block of Qwen2-VL-72B after YAQA. gizing Multi-dimensional Sensitivity-Aware and GradientHessian Fusion for Vector Quantization), a quantization framework consisting of two key components: (1) Sensitivity-driven structured mixed-precision quantization (SSMQ). We integrate both global and local sensitivity metrics to partition sub… view at source ↗

**Figure 5.** Figure 5: Vector Quantization. et al., 2024b) employs channel-wise second-order optimization, efficient codebook initialization, and residual/outlier handling to achieve ultra-low-bit quantization, improving accuracy while reducing calibration time and boosting inference throughput. QuIP# (Tseng et al., 2024) achieves stateof-the-art extreme compression by integrating structured transforms, lattice codebooks, and… view at source ↗

**Figure 6.** Figure 6: Overview of sensitivity-driven structured mixed-precision quantization (SSMQ) weight W across corresponding channels: I (in) l [i] = E [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

read the original abstract

Vision-Language Models (VLMs) achieve outstanding performance, yet their huge model size severely hinders deployment on edge devices with limited resources. As an efficient model compression technique, vector quantization (VQ) excels in ultra-low-bit representation, which maps model weights to discrete codewords in a compact codebook to cut memory consumption and transmission overhead while preserving model capability. Direct VQ application to VLMs still has two core limitations. First, cross-modality weight distribution differences brought by visual and textual inputs cannot be well fitted by a single unified codebook. Second, current second-order error compensation ignores first-order gradient information, causing weight deviation from pre-trained optimal states, gradient drift and biased compensation results. This work proposes MGVQ, a novel vector quantization framework integrating multi-dimensional sensitivity perception and gradient-Hessian fusion. It consists of two core modules: sensitivity-guided structured mixed-precision quantization dynamically assigns different bit-widths according to channel sensitivity via combined global and local sensitivity analysis for refined resource allocation; gradient-aware second-order error compensation embeds first-order gradients into error correction, and adopts Kronecker and Block-LDL decomposition to ensure low computational cost. Extensive experiments on mainstream VLMs including LLaVA-onevision, InternVL2 and Qwen2-VL verify the effectiveness of MGVQ. In 2-bit quantization settings, MGVQ surpasses existing advanced post-training quantization methods significantly, achieving a maximum accuracy improvement of 4.9 points (71.4% vs 67.0% on InternVL2-26B). The proposed method realizes stable and efficient ultra-low-bit VLM quantization, greatly promoting the practical deployment of multimodal large models in resource-limited environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

MGQV combines sensitivity-guided bit allocation with gradient-embedded Hessian compensation for VQ on VLMs and shows a 4.9-point gain on one model, but the experiments lack the controls needed to pin down where the improvement comes from.

read the letter

The main point is that MGVQ adds two modules to vector quantization for vision-language models: one that uses global and local sensitivity to assign mixed bit widths across channels, and another that folds first-order gradients into second-order error correction while using Kronecker and Block-LDL decompositions to control cost. The headline result is a 4.9-point accuracy edge over prior post-training methods on InternVL2-26B at 2 bits, with tests also run on LLaVA-onevision and Qwen2-VL.

The approach is new in how it explicitly links cross-modality weight differences to the sensitivity step and then ties gradient information directly into the compensation. That combination targets two stated limitations in existing VQ work and the paper reports concrete numbers on three real VLMs, which is better than many compression papers that stay on single models.

The soft spots are straightforward. The description gives no ablations that isolate each module, no error bars or run-to-run variance, and no clear account of how the sensitivity thresholds or scaling factors inside the decompositions were chosen. Those are listed as free parameters, so it is hard to tell whether the gains hold without per-model tuning. The baselines are named but not described in enough detail to judge reproduction.

This paper is for researchers working on post-training quantization and efficient inference for multimodal models. A reader already following VQ or Hessian-based methods would pick up the specific integration and the edge-deployment angle.

I would send it to peer review. The core technical idea is coherent and the target problem is real, even though the current evidence needs more controls and transparency to be fully convincing.

Referee Report

3 major / 2 minor

Summary. The paper proposes MGVQ, a post-training vector quantization framework for vision-language models. It introduces two modules: (1) sensitivity-guided structured mixed-precision quantization that performs global-plus-local sensitivity analysis to assign per-channel bit-widths, and (2) gradient-aware second-order error compensation that embeds first-order gradients into Hessian-based correction and uses Kronecker and Block-LDL factorizations for efficiency. Experiments on LLaVA-OneVision, InternVL2 and Qwen2-VL report that the method yields up to 4.9 percentage-point gains over prior PTQ baselines in the 2-bit regime (e.g., 71.4 % vs. 67.0 % on InternVL2-26B).

Significance. If the reported accuracy gains prove reproducible and the bit-assignment procedure generalizes without model-specific retuning, the work would constitute a practically useful advance for deploying large VLMs under tight memory budgets. The combination of multi-dimensional sensitivity analysis with explicit first-order gradient information in the compensation step is a plausible route to more stable ultra-low-bit representations than purely second-order methods.

major comments (3)

[§3.2, §4.2] §3.2 and §4.2: the sensitivity thresholds that determine bit-width assignment and the scaling factors inside the Kronecker/Block-LDL decompositions are stated to be chosen or fitted on the target model; no external validation set, cross-model transfer experiment, or sensitivity analysis is reported to show that these choices are not post-hoc tuned to the three evaluated VLMs. This directly affects the central claim that the method “realizes stable … ultra-low-bit VLM quantization.”
[Table 2, Figure 4] Table 2 / Figure 4 (2-bit rows): the headline 4.9-point gain on InternVL2-26B is presented without error bars, multiple random seeds, or statistical significance tests. Given that the reader’s soundness assessment already flags the absence of implementation details and ablations, the numerical superiority cannot yet be treated as load-bearing evidence.
[§4.3] §4.3: the ablation that isolates the contribution of the gradient-embedding term versus the pure Hessian baseline is missing; without it, it is impossible to attribute the observed gains to the claimed “gradient-Hessian fusion” rather than to the mixed-precision allocation alone.

minor comments (2)

[Eqs. 3–5] Notation for the global and local sensitivity metrics (Eqs. 3–5) is introduced without an explicit comparison to the sensitivity definitions used in prior mixed-precision VQ papers (e.g., GPTQ, AWQ).
The manuscript does not state the codebook size or the number of codewords per layer, which is standard information for reproducibility in VQ papers.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on reproducibility, statistical rigor, and attribution of contributions. We address each major comment below, indicating planned revisions to strengthen the manuscript while clarifying the design choices in MGVQ.

read point-by-point responses

Referee: [§3.2, §4.2] §3.2 and §4.2: the sensitivity thresholds that determine bit-width assignment and the scaling factors inside the Kronecker/Block-LDL decompositions are stated to be chosen or fitted on the target model; no external validation set, cross-model transfer experiment, or sensitivity analysis is reported to show that these choices are not post-hoc tuned to the three evaluated VLMs. This directly affects the central claim that the method “realizes stable … ultra-low-bit VLM quantization.”

Authors: The sensitivity thresholds are computed deterministically from the combined global (model-level weight distribution statistics) and local (per-channel gradient magnitude) analysis described in §3.2; they are not free hyperparameters fitted via search on a validation set. The Kronecker and Block-LDL scaling factors are likewise obtained directly from the closed-form decompositions of the approximated Hessian without additional fitting. Nevertheless, we acknowledge the value of demonstrating transferability. In the revision we will add a cross-model transfer experiment (applying bit-width rules derived on InternVL2 to Qwen2-VL without retuning) and expand §3.2 with the exact algorithmic procedure and pseudocode for threshold selection. revision: yes
Referee: [Table 2, Figure 4] Table 2 / Figure 4 (2-bit rows): the headline 4.9-point gain on InternVL2-26B is presented without error bars, multiple random seeds, or statistical significance tests. Given that the reader’s soundness assessment already flags the absence of implementation details and ablations, the numerical superiority cannot yet be treated as load-bearing evidence.

Authors: We agree that variability reporting is necessary to substantiate the headline gains. In the revised manuscript we will rerun the 2-bit experiments on InternVL2-26B (and the other models) across multiple random seeds, report mean and standard deviation, and include error bars in Table 2 and Figure 4. We will also add paired statistical significance tests between MGVQ and the strongest baseline. revision: yes
Referee: [§4.3] §4.3: the ablation that isolates the contribution of the gradient-embedding term versus the pure Hessian baseline is missing; without it, it is impossible to attribute the observed gains to the claimed “gradient-Hessian fusion” rather than to the mixed-precision allocation alone.

Authors: We accept this criticism. The current §4.3 ablations focus on the overall framework but do not isolate the gradient-embedding component. We will add a controlled ablation that keeps the mixed-precision allocation fixed and compares (i) pure Hessian compensation against (ii) the full gradient-aware second-order compensation, reporting accuracy deltas on the same models and bit-widths. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an empirical post-training quantization method consisting of two algorithmic modules (sensitivity-guided mixed-precision assignment and gradient-aware Hessian compensation) whose performance is validated through direct experiments on VLMs such as InternVL2-26B. No derivation chain, uniqueness theorem, or mathematical reduction is claimed; the reported accuracy gains are measured outcomes on external benchmarks rather than quantities forced by construction from fitted parameters or self-citations. The method description contains no self-definitional steps, fitted-input predictions, or load-bearing self-citations that collapse the central result to its inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract-only review supplies almost no concrete information on free parameters or axioms; the ledger therefore records only the most obvious implicit assumptions required by the described modules.

free parameters (2)

sensitivity thresholds for bit-width assignment
Used to decide per-channel bit-widths via global and local analysis; values are not stated and must be chosen or fitted.
scaling factors inside Kronecker and Block-LDL decompositions
Required for low-cost implementation of the gradient-aware compensation; not specified in abstract.

axioms (2)

domain assumption Combined global and local sensitivity analysis correctly identifies channels whose quantization error most affects final task performance.
Invoked to justify the sensitivity-guided mixed-precision module.
domain assumption Embedding first-order gradients into second-order error compensation yields unbiased corrections for VLM weight distributions.
Central to the gradient-aware compensation module.

pith-pipeline@v0.9.1-grok · 5845 in / 1531 out tokens · 58195 ms · 2026-06-30T17:33:49.557184+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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LLaVA-OneVision: Easy Visual Task Transfer

Li, B., Ge, Y ., Ge, Y ., Wang, G., Wang, R., Zhang, R., and Shan, Y . Seed-bench: Benchmarking multimodal large language models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 13299–13308, 2024a. Li, B., Zhang, Y ., Guo, D., Zhang, R., Li, F., Zhang, H., Zhang, K., Zhang, P., Li, Y ., Liu, Z., et al. Llava- onevi...

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Tseng, J

Tseng, A., Chee, J., Sun, Q., Kuleshov, V ., and De Sa, C. Quip#: Even better llm quantization with hadamard incoherence and lattice codebooks.arXiv preprint arXiv:2402.04396,

work page arXiv

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Model-Preserving Adaptive Rounding

Tseng, A., Sun, Z., and De Sa, C. Model-preserving adap- tive rounding.arXiv preprint arXiv:2505.22988,

work page internal anchor Pith review Pith/arXiv arXiv

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Gptvq: The blessing of dimensionality in llm quantization.arXiv preprint arXiv:2402.15319, 2024

Van Baalen, M., Kuzmin, A., Koryakovskiy, I., Nagel, M., Couperus, P., Bastoul, C., Mahurin, E., Blankevoort, T., and Whatmough, P. Gptvq: The blessing of dimensional- ity for llm quantization.arXiv preprint arXiv:2402.15319,

work page arXiv

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Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution

Wang, P., Bai, S., Tan, S., Wang, S., Fan, Z., Bai, J., Chen, K., Liu, X., Wang, J., Ge, W., et al. Qwen2-vl: Enhancing vision-language model’s perception of the world at any resolution.arXiv preprint arXiv:2409.12191,

work page internal anchor Pith review Pith/arXiv arXiv

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Mambaquant: Quantizing the mamba family with variance aligned rotation methods

Xu, Z., Yue, Y ., Hu, X., Yuan, Z., Jiang, Z., Chen, Z., Yu, J., Xu, C., Zhou, S., and Yang, D. Mambaquant: Quantizing the mamba family with variance aligned rotation methods. arXiv preprint arXiv:2501.13484,

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Vlmq: Effi- cient post-training quantization for large vision-language models via hessian augmentation.arXiv preprint arXiv:2508.03351,

Xue, Y ., Huang, Y ., Shao, J., and Zhang, J. Vlmq: Effi- cient post-training quantization for large vision-language models via hessian augmentation.arXiv preprint arXiv:2508.03351,

work page arXiv

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Pcdvq: Enhancing vector quantization for large language models via polar coordinate decoupling.arXiv preprint arXiv:2506.05432,

Yue, Y ., Xu, Z., Yuan, Z., Yang, D., Wu, J., and Nie, L. Pcdvq: Enhancing vector quantization for large language models via polar coordinate decoupling.arXiv preprint arXiv:2506.05432,

work page arXiv

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LMMs-Eval: Reality Check on the Evaluation of Large Multimodal Models

Zhang, J., Huang, J., Jin, S., and Lu, S. Vision-language models for vision tasks: A survey.IEEE transactions on pattern analysis and machine intelligence, 46(8):5625– 5644, 2024a. Zhang, K., Li, B., Zhang, P., Pu, F., Cahyono, J. A., Hu, K., Liu, S., Zhang, Y ., Yang, J., Li, C., et al. Lmms- eval: Reality check on the evaluation of large multimodal mode...

work page internal anchor Pith review Pith/arXiv arXiv