Paper 2508.10433
We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning
- Published
- Aug 2025
- Research lab
- Independent
- Citations
- 30
- GitHub
- 170 stars
01 In brief
Summary
WE-MATH 2.0 is a unified system to enhance multimodal large language models' (MLLMs) mathematical reasoning.
It integrates a structured knowledge system, model-centric data modeling, and reinforcement learning (RL).
The MathBook Knowledge System is a five-level hierarchy with 491 knowledge points and 1,819 fundamental principles.
MathBook-Standard is a dataset with dual expansions (multi-images per question, multi-questions per image) and GeoGebra-crafted images.
MathBook-Pro defines a three-dimensional difficulty space (step, visual, contextual complexity) and generates 7 progressive variants per problem.
MathBook-RL is a two-stage framework: cold-start fine-tuning for knowledge-oriented chain-of-thought, and progressive alignment RL with average-reward learning and dynamic scheduling (knowledge and modality increments).
MathBookEval is a benchmark covering all 491 knowledge points with diverse reasoning steps.
Experiments show MathBook-7B (based on Qwen2.5-VL-7B) achieves competitive results on four benchmarks (e.g., MathVista 73.0, We-Math 48.4) and strong performance on MathBookEval, using only 9.8K training samples, demonstrating efficient generalization.
Ablations confirm both RL stages contribute, and SFT is crucial for unlocking RL potential.
02 From the paper
Abstract
Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities across various tasks, but still struggle with complex mathematical reasoning. Existing research primarily focuses on dataset construction and method optimization, often overlooking two critical aspects: comprehensive knowledge-driven design and model-centric data space modeling. In this paper, we introduce We-Math 2.0, a unified system that integrates a structured mathematical knowledge system, model-centric data space modeling, and a reinforcement learning (RL)-based training paradigm to comprehensively enhance the mathematical reasoning abilities of MLLMs. The key contributions of We-Math 2.0 are fourfold: (1) MathBook Knowledge System: We construct a five-level hierarchical system encompassing 491 knowledge points and 1,819 fundamental principles. (2) MathBook-Standard & Pro: We develop MathBook-Standard, a dataset that ensures broad conceptual coverage and flexibility through dual expansion. Additionally, we define a three-dimensional difficulty space and generate 7 progressive variants per problem to build MathBook-Pro, a challenging dataset for robust training. (3) MathBook-RL: We propose a two-stage RL framework comprising: (i) Cold-Start Fine-tuning, which aligns the model with knowledge-oriented chain-of-thought reasoning; and (ii) Progressive Alignment RL, leveraging average-reward learning and dynamic data scheduling to achieve progressive alignment across difficulty levels. (4) MathBookEval: We introduce a comprehensive benchmark covering all 491 knowledge points with diverse reasoning step distributions. Experimental results show that MathBook-RL performs competitively with existing baselines on four widely-used benchmarks and achieves strong results on MathBookEval, suggesting promising generalization in mathematical reasoning.