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VIG: Visual Information Gain as a Reward Signal for Multimodal Chain-of-Thought Compression

Wen Luo, Xiaohan Yi, Xiaotao Huang, Liqun Huang

arXiv:2608.21883v1cs.CV

TL;DR

Multimodal reasoning chains contain visually disengaged tokens that increase inference cost and can undermine correctness, while existing compression methods do not measure image dependence. VIG uses an online two-pass information-theoretic reward to score visual information in each reasoning token, and it consistently improves the accuracy–efficiency trade-off across the evaluated benchmarks and model sizes.

  • Problem

    Long multimodal CoT traces contain repeated descriptions, self-reflection, and other tokens that do not consult the image, while existing compression methods lack a per-token measure of visual grounding.

  • Method

    VIG measures each reasoning token’s visual information gain from the entropy difference between policy passes with and without visual tokens, then uses the aggregate as an online GRPO reward.

  • Results

    Across six multimodal benchmarks and three Qwen3-VL-Thinking sizes, VIG consistently improves the accuracy–efficiency trade-off and reaches 64.92% average accuracy with 52.42 ACC per 1k tokens on Qwen3-VL-8B-Thinking.

  • Takeaways & Limitations

    Efficient multimodal reasoning emerges by increasing visual information density, with chain shortening occurring as a byproduct rather than through a direct length constraint.

  • Takeaways & Limitations

    VIG requires an additional text-only forward pass during RL training, depends on separating visual and textual tokens, and measures visual dependence rather than visual correctness or counterfactual necessity.

Abstract

from arXiv · show

Multimodal large reasoning models often rely on long Chain-of-Thought (CoT) traces in which a substantial fraction of tokens, such as repeated visual descriptions, self-reflection, and other visually-disengaged filler, inflate inference cost without contributing to the answer. Existing CoT compression methods optimize output length but never measure whether a reasoning token is actually grounded in the image. We propose \textbf{VIG} (Visual Information Gain), an information-theoretic GRPO reward that scores each reasoning token by how much the image reduces its predictive uncertainty. VIG is computed online from two forward passes of the same policy, one with and one without the image, so no reference chains, external annotations, or auxiliary reward models are needed. Across six main multimodal reasoning benchmarks and three Qwen3-VL-Thinking model sizes (2B/4B/8B), plus an additional R1-Onevision-Bench evaluation on 8B, VIG consistently improves the accuracy--efficiency trade-off, supporting our central claim: \emph{efficient multimodal reasoning emerges from raising visual information density, where every reasoning token earns its place by anchoring to the image, rather than from imposing a length budget.} Our source code is available at https://github.com/chaser682/vig.

1 Introduction

Multimodal reasoning chains can be unnecessarily long because many tokens do not consult the image, increasing cost and sometimes harming correctness. VIG addresses this by rewarding token-level visual dependence, yielding consistent accuracy–efficiency gains across benchmarks and model sizes.

  • Motivation: Long multimodal CoT traces often contain repeated descriptions, metacognition, and rephrased visual relationships that never consult the image.These tokens inflate computation and can make reasoning less accurate than shorter, more visually grounded chains.
  • Motivation: Over-reasoning increases latency and can accumulate perceptual errors that talk models out of initially correct visual conclusions.The paper attributes this problem to training paradigms that encourage long reasoning chains.
  • Motivation: 823 tokens produced an incorrect geometry answer for the base model, while L1 used 412 tokens and VIG used 105 tokens to recover the correct answer.The example illustrates that shortening alone trims self-doubt, whereas VIG targets visually ungrounded reasoning.
  • Method: VIG scores each reasoning token by how much the image reduces its predictive uncertainty, using two policy forward passes with and without visual tokens.The per-token entropy difference is averaged over the reasoning block and used as a GRPO reward; no reference chains, annotators, or auxiliary models are required.
  • Results: 64.92% average accuracy and 52.42 ACC per 1k tokens let VIG Pareto-dominate evaluated baselines on Qwen3-VL-8B-Thinking.Compared with ThinkPrune, VIG improves accuracy by +2.37% and efficiency by +39.4%.
  • Results: VIG reaches a new accuracy–efficiency Pareto frontier across six benchmarks and three Qwen3-VL-Thinking sizes, while ranking first overall on R1-Onevision-Bench.On that benchmark, it ranks first or tied-first in three of five subject categories.

2 Related Work

Multimodal CoT compression methods use textual or architectural signals, but these approaches do not measure whether reasoning tokens depend on the image. VIG introduces an image-dependent reward to target that gap.

  • Multimodal reasoning models: Multimodal reasoning systems extend long-CoT training and structured visual reasoning, but stronger reasoning can bring substantially longer chains.The related work includes systems based on stage-wise decomposition, search, and R1-style reasoning.
  • Compression methods: Training-based methods incorporate compression into supervised or reinforcement-learning objectives, including token ranking, length penalties, and related controls.These methods differ in whether they operate at token level or through broader training objectives.
  • Compression methods: Prompt-based compression controls chain length through instructions or budget flags, compressing by truncation without modifying model parameters.TALE estimates a per-question token budget, while Kimi k1.5 toggles between long and short reasoning.
  • Compression methods: Latent and architectural alternatives bypass tokenized CoT or compress it through hidden states, gist tokens, carryover state, or chunk-level inference.These approaches typically require architectural changes or inference-time modifications.
  • Research gap: Existing approaches use purely textual compression signals and do not measure how much each reasoning token depends on the image.Prior information-theoretic objectives were applied to visual-encoder features rather than multimodal reasoning tokens.

3 Method

VIG scores reasoning tokens by the uncertainty reduction provided by the image, aggregates these scores over the reasoning chain, and uses the result with format and accuracy rewards in GRPO. Its two-pass computation requires the same policy with and without visual tokens, while chain shortening emerges from rewarding visual grounding rather than directly penalizing length.

  • Token-level visual information gain: VIG measures each reasoning token’s visual information gain as the uncertainty removed by conditioning on the image.A high-VIG token is uncertain without the image but confident with it; near-zero VIG indicates derivability from textual context alone.
  • Token-level visual information gain: The token-level score is the difference between text-only and vision-conditioned next-token entropies.Htxt(tτ) is the entropy without visual input, while Hvis(tτ) is the entropy with the question, image, and preceding context.
  • Sequence-level reward: VIG is aggregated over the <think> block using a clipped token-level mean, providing a length-normalized estimate of chain-level visual information.The unclipped mean follows from the chain rule of mutual information, while clipping constrains the practical reward range.
  • Two-pass forward computation: The reward is computed online by two forward passes of the same policy: one with the full multimodal input and one with visual tokens removed.The token-level entropy differences are masked to the <think> block, averaged, and clipped; the vision-stripped pass requires no gradients.
  • GRPO reward: GRPO combines visual information gain with format compliance and answer correctness to encourage well-formed, correct, visually grounded responses.The format term rewards the desired <think>/<answer> structure, while the accuracy term checks the extracted answer against the ground truth.
  • GRPO reward: VIG suppresses visually disengaged filler and yields shorter, denser reasoning chains without introducing an explicit length penalty.The method retains tokens that directly read or relate visual evidence while suppressing metacognitive openers and repeated restatements.

4 Experiments

VIG is evaluated across multimodal reasoning benchmarks, model sizes, non-mathematical visual tasks, and targeted ablations. It improves accuracy–efficiency trade-offs by increasing visual information density, while visual density is associated with shorter, more accurate reasoning chains.

  • Experimental Setup: VIG is compared with Base, GRPO, L1, TALE, and ThinkPrune across three Qwen3-VL-Thinking sizes and six main benchmarks.The evaluation reports accuracy, average reasoning-chain length, and efficiency measured as accuracy per kilotoken.
  • Main Results: 64.92% AvgACC and 52.42 AvgEff on Qwen3-VL-8B-Thinking surpass ThinkPrune by +2.37% accuracy and +39.4% efficiency while shortening AvgTLen by 397 tokens.Compared with plain GRPO, VIG reduces the average chain from 1975 to 1524 tokens and raises accuracy by +2.04%.
  • Main Results: 56.79 overall accuracy and 29.19 AvgEff on R1-Onevision-Bench make VIG best overall, with first-place or tied-first results across several subject categories.VIG uses fewer tokens than every baseline on four of five subjects and exceeds the strongest baseline by +3.60% on Physics and +5.51% on Mathematics.
  • Main Results: VIG produces the shortest chains and highest accuracy on RealWorldQA and OCRBench, reducing output tokens by 52% and 66% relative to the base model.The authors interpret these results conservatively because accuracy gaps among stronger methods fall within noise.
  • Ablation Studies: Removing VIG reduces AvgEff from 52.42 to 36.44 and AvgACC by 2.04 points, while replacing the no-image pass with masking costs 1.94 accuracy points and 13.72 efficiency points.The no-image comparison yields a sharper information-theoretic contrast than partial masking.
  • Visual Density Analysis: Average per-token VIG decreases with chain length (r = −0.569, p < 0.001), while WeMath quintiles rise from 60.1% to 91.7% accuracy and fall from 2574 to 200 tokens.The ACC–VIG relationship is reported as descriptive and partly mediated by chain length and item difficulty.

5 Conclusion

VIG is an information-theoretic reward that measures each reasoning token’s dependence on visual input and trains multimodal models to increase visual density. Across broad evaluations, it improves the accuracy–efficiency trade-off without relying on reference chains or external annotators.

  • VIG measures how much each reasoning token depends on the image, reframing multimodal CoT compression as increasing visual density.
  • The reward is computed online from two forward passes of the same policy and integrates with GRPO without reference chains or external annotators.
  • Across six multimodal benchmarks and three Qwen3-VL-Thinking sizes, VIG consistently improves the accuracy–efficiency trade-off.
  • Efficient multimodal CoT generation requires making each token rely more on visual evidence, not merely reducing the number of tokens.

Limitations

VIG’s practical scope is constrained by extra training computation and model-specific handling of visual and textual tokens. Its visual-dependence score also does not guarantee correctness, necessity, or transfer across architectures and settings.

  • VIG requires an additional text-only forward pass during RL training, increasing optimization cost relative to standard GRPO.
  • The method depends on cleanly separating visual and textual tokens, making implementation somewhat model-specific.
  • VIG measures visual dependence rather than visual correctness or counterfactual necessity, so high scores can accompany hallucinated visual readings.
  • Because low-VIG sentences can remain load-bearing after compression, VIG is suited to training-time output shaping rather than post-hoc pruning.
  • The study covers static image reasoning with Qwen3-VL-Thinking models, leaving cross-architecture generality unresolved.

C Proof of VIG Non-Negativity

At the population level, VIG is a conditional mutual-information quantity and is therefore non-negative. Practical plug-in estimates can occasionally become negative because the policy is imperfect, text-only inputs are out of distribution, and finite-precision computation adds noise.

  • Algorithm 1 computes RVIG by comparing vision- and text-pass entropies, masking the think block, averaging the differences, and clipping to [−1, +1].
  • VIG(tτ) equals the conditional mutual information I(tτ; I | q, t<τ), which is non-negative by the data processing inequality.
  • The population inequality need not hold for empirical policy estimates because the text-only pass evaluates the network on an out-of-distribution input.
  • Negative empirical VIG is attributed to policy mis-specification, phantom attention or higher entropy without visual tokens, and numerical rounding noise.
  • Negative values affect less than ∼1% of think-block tokens and are concentrated near zero, motivating clipping and block-level averaging.

D Data Details

The evaluation uses seven reasoning benchmarks in total, with six for the main comparison and one for subject-level evaluation. RL training draws from MMStar, MathVista, and LogicVista, while the evaluation suite spans mathematics, broad multimodal knowledge, perception, and logic.

  • The study evaluates seven reasoning benchmarks: six for the main comparison and one additional benchmark with subject-level evaluation.
  • The RL training mixture uses MMStar, MathVista, and LogicVista.
  • WeMath evaluates visual mathematics, MMMU spans college-level disciplines, and MathVision targets multimodal mathematical reasoning.
  • MMStar emphasizes fine-grained perception, spatial reasoning, and image–text alignment, while MathVista covers charts, geometry, symbolic reasoning, and visual word problems.

E Implementation Details

The experiments compare VIG with standard, length-based, prompting, and pruning baselines, while probing the signal’s behavior across item strata and sentence types. VIG is computed through paired image and no-image policy passes and evaluated with deletion probes.

  • VIG implementation: VIG scores token-level visual information gain by contrasting the same policy’s image-conditioned and text-only predictions.The entropy difference is restricted to the <think> block, averaged over tokens, and clipped to form RVIG.
  • Controls: The confidence-only control replaces visual contrast with negative image-conditioned entropy to test whether entropy or brevity shaping alone explains gains.It shares VIG’s pipeline, data, seed, and step count.
  • Stratification: Evaluation separates text-solvable from vision-required items using the base model without the image, then re-scores VIG and GRPO within each stratum.Confidence intervals come from a 10k paired bootstrap over items.
  • Sentence typing: Mean VIG is highest for visual sentences at 0.153 and lowest for algebra sentences at 0.065 across 70,754 VIG-8B WeMath sentences.Meta and other sentences score 0.106 and 0.088, respectively.
  • Deletion probe: Deletion probes rank completed-chain sentences by VIG and re-decode from prefixes after removing specified fractions.The probe tests both image-retained and image-removed re-decoding conditions.

F.2 Interpreting the Deletion Asymmetry

Deletion results reveal that VIG’s apparent importance reverses after visual-density training: low-VIG algebraic sentences can be more answer-critical than high-VIG visual readouts. The comparison with GRPO and other methods bounds this interpretation and exposes evaluation limitations.

  • F.2 Interpreting the Deletion Asymmetry: Deleting lowest-VIG sentences is most damaging on VIG-trained chains, contrary to a straightforward token-importance interpretation.The result is reported on the quantile-deletion probe.
  • F.2 Interpreting the Deletion Asymmetry: Low-VIG sentences are enriched in visually ungrounded algebra and derivation, so removing them breaks arithmetic; high-VIG readouts remain recoverable from the image.High-VIG deletion costs only 1.67 points even when the image is also removed.
  • F.2 Interpreting the Deletion Asymmetry: On GRPO-generated chains, the deletion ordering reverses, indicating that VIG tracks answer-critical visual content before visual information has been compressed away.The authors identify chain state as the source of the asymmetry.
  • F.3 Scope of the Comparison: At 1,297 tokens, VIG reaches 71.37 AvgACC versus 63.39 at 1,100 tokens for the released VPPO-8B checkpoint.VPPO produces slightly shorter chains and a higher efficiency ratio, while VIG retains substantially higher accuracy.
  • F.3 Scope of the Comparison: The VPPO comparison is not fully matched because the checkpoint uses different model and data conditions, leaving reproduction for future work.The passage explicitly treats the comparison as indicative.
  • Failure cases: On MathVision, VIG does not lead accuracy at 8B, while retaining the shortest chains; at larger decoding budgets, accuracy differences narrow but its efficiency advantage persists.At 8B, ThinkPrune scores 32.57, TALE 32.50, and VIG 32.20; margins are within noise.

G Training Cost

VIG adds computational overhead during training because it requires a second forward pass, but shorter outputs can amortize that cost during deployment. The section also documents qualitative evidence that VIG preserves visual grounding while reducing chain length.

  • G Training Cost: VIG requires a second text-only forward pass per rollout sample, giving a theoretical worst-case overhead of 2× plain GRPO.The practical gap is smaller because visual-token spans are removed before the second forward.
  • G Training Cost: VIG adds only ∼17% per-step wall-clock cost relative to plain GRPO and converges within the same 500-step budget.Its relative cost is comparable to L1 at 1.05× and ThinkPrune at 1.01×, without additional rollouts.
  • G Training Cost: Training VIG costs 6.0 additional GPU-hours, while inference emits 1,297 tokens per query versus 1,751 for plain GRPO.This corresponds to a saving of approximately 454 tokens per request under the stated protocol.
  • Qualitative comparisons: A sentence reading a ruler scores +0.90 VIG while answer-bearing arithmetic scores +0.004; image-driven generation can still misread a protractor.The failure example predicts 50° instead of the gold 40° despite visual dependence.
  • Qualitative comparisons: The qualitative comparisons show VIG producing shorter reasoning chains while retaining decisive visual evidence and avoiding unnecessary self-reflection.The same pattern is reported across side-by-side Base, L1, and VIG examples.

I Datasets and Licenses

The evaluation uses publicly released multimodal reasoning benchmarks under research-permissive licenses and reports qualitative examples spanning coordinate geometry and shaded-area questions.

  • I Datasets and Licenses: The evaluation benchmarks are publicly released for research use under Apache-2.0, MIT, or CC-BY-NC-4.0 variants.The listed datasets include WeMath, MathVision, DynaMath, Geo3K, MMMU, MMK12, and R1-Onevision-Bench.
  • I Datasets and Licenses: The examples cover coordinate reflection, shaded-area calculation, and comparative reasoning outputs from Base, L1, and VIG.The coordinate example presents distinct Base, L1, and VIG reasoning traces.
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