MathVis-Fine: Aligning Visual Supervision with Necessity via Progressive Dependency-Guided Training for Multimodal Mathematical Reasoning
Authors: Wanshi Xu, Haokun Zhao, Haidong Yuan, Songjun Cao, Long Ma
Organizations: School of ECE, Peking University · College of Computer Science and Artificial Intelligence, Fudan University · School of Software and Microelectronics, Peking University · Tencent Youtu Lab
Chain-of-Thought (CoT) reasoning has extended from purely linguistic domains to multimodal scenarios; however, existing approaches often treat visual inputs as homogeneous or auxiliary signals, failing to capture the intricate and sample-specific dependencies between text and images in mathematical problem-solving. This gives rise to two core issues: first, the supervisory signals for visual content are generalized and coarse-grained, lacking adaptation to the actual necessity of visual information in each sample; second, training feedback becomes inaccurate when visual rewards are uniformly applied without distinguishing the complementary relationships among inputs. These limitations hinder models from achieving precise multimodal reasoning. In this work, we propose a framework for modeling fine-grained visual dependencies in mathematical reasoning. We first construct the MathVis-Fine dataset, augmenting fine-grained visual annotations with visual dependency ratings. Building upon this dataset, we introduce a two-stage progressive visual enhancement training paradigm that balances answer correctness rewards and visual grounding rewards according to the intrinsic visual dependency level of each sample, thereby mitigating reward bias and improving supervision accuracy. Extensive experiments demonstrate that the MathVis-Fine framework effectively enhances visual perception progressively based on visual dependency, offering a more precise training framework for multimodal mathematical reasoning. We will release the dataset upon acceptance.
Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.
Chain-of-thought (CoT) reasoning has proven effective for enhancing problem-solving in large language models. However, when applied to multimodal LLMs (MLLMs), existing CoT approaches suffer from a fundamental limitation: they perform reasoning entirely in text without accessing visual features during the reasoning process. After initial visual encoding, image information becomes inaccessible, forcing models to reason based solely on whatever was captured in the initial description, which forms a `vision-blind reasoning' paradigm that limits fine-grained visual extraction, error verification, and adaptive attention. We propose Text-Visual Interleaved Chain-of-Thought (TVI-CoT), a framework that enables explicit interleaving of textual reasoning and visual feature access through learnable control tokens <THINK>, <LOOK> and <ANSWER>. These tokens allow dynamic switching between reasoning and visual grounding, attending to relevant image regions conditioned on the evolving reasoning state. Experiments on eight benchmarks demonstrate state-of-the-art results among MLLM-based CoT methods and notable performance boost compared to the baseline: +6.1% on MMMU, +3.8% on MathVerse, +3.4% on MathVista, and +3.4% on ScienceQA. Code is available at https://github.com/hulianyuyy/TVI-CoT.
Scaling reinforcement learning for visual mathematical reasoning requires more than generating harder questions: as data volume grows, the reward labels themselves must remain reliable. Yet existing data pipelines scale supervision while trusting the labeller, and policy-side methods assume the underlying answers are already correct. We instead treat scaling as a verifiable data-construction problem and decouple two axes before any policy update: prompt difficulty, expanded by route-specific evolution operators, and answer reliability, enforced by offline hypothesis-test falsification. We instantiate this as VeriEvol, an iterative framework with two extensible components: a type-aware evolution module that rewrites low-difficulty image-question seeds into harder, image-grounded prompts; and HTV-Agent, a verifier that accepts an answer only after multi-source counter-evidence has failed to refute it. The resulting verified data scales in volume, extends by adding evolution routes or verifier channels, and plugs directly into existing GRPO-style RL recipes. On a five-benchmark visual-math suite, scaling evolved SFT data from 10K to 250K samples raises the mean accuracy from 35.42 to 54.73; then, with backbone, SFT initialization, and GRPO recipe held fixed, VeriEvol adds a cumulative +3.88 over an un-evolved RL baseline, of which +1.82 comes from evolved prompts and +2.06 from the HTV-Agent verifier. We release the prompts, data, models, code, and the full verifier trace of every sample, so that downstream work can scale and audit the pipeline rather than only inspect its outputs.