Multimodal Mathematical Reasoning with Diverse Solving Perspective

TL;DR

This paper introduces a new dataset and model for multimodal mathematical reasoning that emphasizes diverse solution strategies and internal reflections, leading to improved accuracy and reasoning diversity.

Contribution

The work presents MathV-DP, a dataset capturing multiple solution trajectories, and Qwen-VL-DP, a model trained with a novel reinforcement learning approach to enhance reasoning diversity.

Findings

Qwen-VL-DP outperforms prior models in accuracy.

The model generates more diverse solutions.

Incorporating diverse perspectives improves reasoning quality.

Abstract

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.