ViRC: Enhancing Visual Interleaved Mathematical CoT with Reason Chunking

TL;DR

This paper introduces ViRC, a framework that structures multimodal mathematical reasoning into logical units, improving the reasoning capabilities of large language models by mimicking human problem-solving strategies.

Contribution

We propose a Reason Chunking mechanism and a new dataset, CRUX, to enhance multimodal mathematical reasoning in LLMs, inspired by cognitive science principles.

Findings

ViRC-7B outperforms baselines by 18.8% on mathematical benchmarks.

The Reason Chunking approach improves intra-unit coherence and visual reasoning integration.

The CRUX dataset provides annotated reasoning units to facilitate training.

Abstract

CoT has significantly enhanced the reasoning ability of LLMs while it faces challenges when extended to multimodal domains, particularly in mathematical tasks. Existing MLLMs typically perform textual reasoning solely from a single static mathematical image, overlooking dynamic visual acquisition during reasoning. In contrast, humans repeatedly examine visual image and employ step-by-step reasoning to prove intermediate propositions. This strategy of decomposing the problem-solving process into key logical nodes adheres to Miller's Law in cognitive science. Inspired by this insight, we propose a ViRC framework for multimodal mathematical tasks, introducing a Reason Chunking mechanism that structures multimodal mathematical CoT into consecutive Critical Reasoning Units (CRUs) to simulate human expert problem-solving patterns. CRUs ensure intra-unit textual coherence for intermediate proposition verification while integrating visual information across units to generate subsequent propositions and support structured reasoning. To this end, we present CRUX dataset by using three visual tools and four reasoning patterns to provide explicitly annotated CRUs across multiple reasoning paths for each mathematical problem. Leveraging the CRUX dataset, we propose a progressive training strategy inspired by human cognitive learning, which includes Instructional SFT, Practice SFT, and Strategic RL, aimed at further strengthening the Reason Chunking ability of the model. The resulting ViRC-7B model achieves a 18.8% average improvement over baselines across multiple mathematical benchmarks. Code is available at https://github.com/Leon-LihongWang/ViRC.