Func-R1: Incentivizing Mathematical Function Reasoning in Multimodal Large Language Models

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 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.

Reasoning in vision-language models (VLMs) has recently attracted significant attention due to its broad applicability across diverse downstream tasks. However, it remains unclear whether the superior performance of VLMs stems from genuine vision-grounded reasoning or relies predominantly on the reasoning capabilities of their textual backbones. To systematically measure this, we introduce CrossMath, a novel multimodal reasoning benchmark designed for controlled cross-modal comparisons. Specifically, we construct each problem in text-only, image-only, and image+text formats guaranteeing identical task-relevant information, verified by human annotators. This rigorous alignment effectively isolates modality-specific reasoning differences while eliminating confounding factors such as information mismatch. Extensive evaluation of state-of-the-art VLMs reveals a consistent phenomenon: a substantial performance gap between textual and visual reasoning. Notably, VLMs excel with text-only inputs, whereas incorporating visual data (image+text) frequently degrades performance compared to the text-only baseline. These findings indicate that current VLMs conduct reasoning primarily in the textual space, with limited genuine reliance on visual evidence. To mitigate this limitation, we curate a CrossMath training set for VLM fine-tuning. Empirical evaluations demonstrate that fine-tuning on this training set significantly boosts reasoning performance across all individual and joint modalities, while yielding robust gains on two general visual reasoning tasks. Source code is available at https://github.com/xuyige/CrossMath.