Extending Reinforcement Learning with Verifiable Rewards (RLVR) to multimodal large language models (MLLMs) faces a fundamental challenge: their responses inherently interleave perception-related tokens, which ground visual content, with reasoning-related tokens, which construct reasoning chains. These token types instantiate distinct yet interdependent capacities -- visual grounding and symbolic reasoning -- making isolated optimization insufficient. Through token-level empirical analysis, we demonstrate that optimizing either perception- or reasoning-only tokens consistently underperforms full optimization, underscoring their inherent coupling. To address this, we propose a plug-and-play Token-Reweighting (ToR) strategy that explicitly models this interdependence by identifying critical tokens of both types and dynamically reweighting them during RLVR training. Applied on top of existing methods (e.g., GRPO and DAPO), ToR delivers consistent performance gains across multiple multi-modal reasoning benchmarks, achieving state-of-the-art performance with both accurate visual grounding and coherent reasoning.
Figures & tables
Figure 1: MLLM responses typically involve two types of critical tokens: (1) reasoning-related tokens to construct reasoning chains, and (2) perception-related tokens to ground visual content.
Figure 2: Performance comparison over the wemath benchmark ( Qiao et al., 2024 ) when optimizing different token types with GRPO ( Shao et al., 2024 ) . Results across selection ratios 20%, 30%, or 50% show that optimizing either reasoning-only or perception-only tokens underperforms all tokens. Qualitative examples are selected from the best-performing checkpoints.
Figure 3: Comparison of perception strength and reasoning uncertainty under different token ratios during GRPO optimization. (a) Reasoning-token-only optimization suffers from limited perception capacity. (b) Perception-token-only optimization is sensitive to high reasoning uncertainty. (c) Token reweighting yields a balanced regime by adaptively trading off perception strength and reasoning uncertainty, where the shaded region indicates effective optimization outcomes. Dashed lines denote the balance where increased perception strength compensates for reasoning uncertainty.
αr
HalluBench
MathVerse
WeMath
MathVision
MathVista
20%
62.8
49.3
63.9
26.5
69.2
30%
65.1
50.7
65.6
27.0
70.0
40%
66.1
50.1
65.9
26.3
69.4
50%
67.1
50.4
66.0
27.0
68.7
60%
67.1
50.0
67.1
27.3
70.3
70%
67.5
50.8
67.3
26.7
70.0
Table 1: Performance comparison with different ratios of reasoning-related tokens ( αr ). We vary the proportion of reasoning-related tokens from 20% to 80%.
αp
HalluBench
MathVerse
WeMath
MathVision
MathVista
20%
65.9
38.6
61.4
22.7
65.5
30%
69.3
44.9
64.8
24.5
67.8
40%
67.8
44.7
65.9
25.1
67.4
50%
68.3
39.5
62.9
27.6
68.7
60%
68.1
45.1
65.8
25.0
67.4
70%
65.1
45.8
66.8
25.2
68.9
Table 2: Performance comparison with different ratios of perception-related tokens ( αp ). We vary the proportion of perception-related tokens from 20% to 80%.
γp
HalluBench
MathVerse
WeMath
MathVision
MathVista
0.1
66.5
50.8
65.5
27.3
69.7
0.3
69.1
52.1
67.4
28.6
70.8
0.5
71.3
53.0
68.7
28.3
71.9
0.7
70.5
51.1
68.1
27.5
70.8
0.9
72.2
50.9
67.0
27.2
71.4
1.1
71.3
49.9
67.3
26.9
69.3
Table 3: Performance under different combinations of reasoning and perception tokens. We vary the perception-related weight from 0.1 to 1.5 while keeping the reasoning-related weight fixed at 1.0.
Model
Data Size
MathVerse
MathVision
MathVista
WeMath
HalluBench
Open-source Models
InternVL-2.5-8B ( Chen et al., 2024 )
-
39.5
19.7
64.4
-
67.3
InternVL-3-8B ( Zhu et al., 2025 )
-
39.5
29.3
71.6
37.1
-
LLaVA-OneVision-7B ( Li et al., 2025a )
-
26.2
-
63.2
-
48.4
Qwen2.5-VL-7B-Instruct ( Bai et al., 2025 )
-
46.2
25.0
67.5
63.1
64.6
RLVR on Qwen-2.5-VL-7B
Table 4: Performance comparison of multi-modal LLMs under different model and data scales. Following existing works ( Liu et al., 2025a ; Xiao et al., 2025 ) , we highlight the data size with blue and red for SFT and RL , respectively. The best value in each column is shown in bold , and the second-best is underlined .
Figure 4: Comparison of optimization behaviors under different token selection strategies. Vanilla GRPO optimizes uniformly across all tokens. Reasoning-only and perception-only optimization concentrate on a single token type, leading to imbalanced training. Token reweighting jointly emphasizes reasoning- and perception-related tokens, achieving a more balanced optimization.
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 9Figure 10Figure 11
Perception Proxy
HallusionBench
WeMath
MathVerse
Avg. Gain
Baseline (GRPO)
69.8
67.4
50.8
–
Prob Diff (best visual grounding)
71.8 (+2.0)
68.5 (+1.1)
52.6 (+1.8)
+1.6%
Entropy Diff (best info-theoretic)
70.9 (+1.1)
67.9 (+0.5)
51.5 (+0.7)
+0.8%
Logp Diff (best balance)
72.4 (+2.6)
68.9 (+1.5)
53.0 (+2.2)
+2.1%
Appendix
Table 5: Comparison of different perception proxies within the ToR framework. Performance is reported on HallusionBench, WeMath, and MathVerse. Gains are computed relative to the GRPO baseline.
Figure 11: Correlation heatmaps between different image token selection strategies over the validation set.
Figure 12: Correlation heatmaps between different image token selection strategies over the hallubench benchmark.
Figure 13: Correlation heatmaps between different image token selection strategies over the wemath benchmark.
Figure 14: Correlation comparison across layers between different image token selection strategies over the validation set.
Figure 15: Correlation comparison across layers between different image token selection strategies over the hallubench benchmark.
Figure 16: Correlation comparison across layers between different image token selection strategies over the wemath benchmark.
Figure 17: violin plot between different image token selection strategies over the validation set.
Figure 18: violin plot between different image token selection strategies over the Hallubench benchmark.
Figure 19: violin plot between different image token selection strategies over the wemath benchmark.
Figure 20: Distribution of selected tokens over the sampled rollouts, where we employ the Qwen-VL-2.5 7B model with a batch of 512 samples, each sample generates 16 rollout responses.
Reinforcement Learning with Verifiable Rewards (RLVR) has become an effective paradigm for improving the reasoning capability of Large Vision-Language Models (LVLMs). However, existing RLVR methods primarily rely on trajectory-level outcome rewards, which assign identical learning signals across all generated tokens. This coarse-grained credit assignment is fundamentally mismatched to multimodal reasoning, where only a sparse subset of tokens is causally grounded in visual evidence. Consequently, these pivotal perceptual tokens receive weak supervision and are often overwhelmed by language priors or reasoning-template tokens. To address this limitation, we propose Perception-Reinforced Policy Optimization (PRPO), a token-level reinforcement learning framework that explicitly identifies and reinforces pivotal perceptual tokens within long-horizon multimodal reasoning trajectories. PRPO introduces Robust Visual Dependency (RVD), a principled metric that identifies tokens whose predictions are both visually grounded and perturbation-stable, filtering out brittle or noisy visual tokens. Based on RVD, we further propose Perceptual Advantage Reshaping (PAR), a token-level credit assignment technique that amplifies perceptually informative tokens while preserving stable gradients for non-perceptual tokens. Extensive experiments on seven multimodal reasoning benchmarks demonstrate that PRPO consistently outperforms strong LVLM baselines across both 3B and 7B model scales, achieving average gains of 23.3% and 21.1%, respectively. PRPO achieves state-of-the-art performance with improved training efficiency and stronger cross-task generalization. Our findings highlight the importance of fine-grained credit assignment for scalable multimodal reinforcement learning.
Reinforcement Learning with Verifiable Rewards (RLVR) has improved the reasoning capabilities of Multimodal Large Language Models (MLLMs), yet existing frameworks rely on coarse, sequence-level reward signals that lack the fine-grained supervision over the visually-grounded steps within a multimodal reasoning chain. We investigate this gap through the lens of two token-level metrics: visual dependency (i.e. how much a token's prediction relies on the input image features) and predictive entropy. Our empirical analysis reveals two key findings: (1) correct reasoning chains exhibit a markedly sharper entropy reduction as visual grounding intensifies, compared to incorrect ones; (2) pivotal tokens, those whose misprediction triggers reasoning collapse, are statistical outliers in the joint distribution of visual dependency and predictive entropy derived from correct chains. Motivated by these findings, we propose token-level perception-grounded advantage estimation (TPAE), which estimates token-level advantages by measuring each token's statistical consistency with the vision-entropy patterns of correct rollouts. TPAE leverages this granular score to modulate the sequence-level advantage, producing a fine-grained supervision signal that can be integrated into various RLVR frameworks. Extensive experiments on seven benchmarks show that TPAE consistently outperforms leading strong baselines, yielding more stable and efficient optimization for multimodal reasoning. The code is publicly available at https://github.com/Zhihan72/TPAE.
Zhihan Zhang, Lizi Liao
Singapore Management University Singapore, Singapore
Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for multimodal large language models (MLLMs) have mainly focused on improving final answer correctness and strengthening visual grounding. However, a critical bottleneck remains: although models can attend to relevant visual regions, they often fail to effectively incorporate visual evidence into subsequent reasoning, leading to reasoning chains that are weakly grounded in visual facts. To address this issue, we propose Trajectory-Guided Reinforcement Learning (TGRL), which guides the policy model to integrate visual evidence into fine-grained reasoning processes using expert reasoning trajectories from stronger models. We further introduce token-level reweighting and trajectory filtering to ensure stable and effective policy optimization. Extensive experiments on multiple multimodal reasoning benchmarks demonstrate that TGRL consistently improves reasoning performance and effectively bridges the gap between visual perception and logical reasoning.
Jinda Lu, Junkang Wu, Jinghan Li +6
University of Science and Technology of China · Pecking University · Institute of Software, Chinese Academy of Sciences