We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning

Multimodal large language models (MLLMs) have demonstrated impressive capabilities across various tasks but still struggle with complex mathematical reasoning. Prior work has mainly focused on dataset construction and method optimization, while often overlooking two critical aspects: comprehensive knowledge-driven design and model-centric data space modeling. We introduce WE-MATH 2.0, a unified system that integrates a structured mathematical knowledge hierarchy, model-centric data space modeling, and a reinforcement learning (RL)-based training paradigm to enhance the mathematical reasoning abilities of MLLMs. Our contributions are fourfold: (1) MathBook Knowledge System: a five-level hierarchy covering 491 knowledge points and 1,819 fundamental principles; (2) MathBook-Standard and MathBook-Pro: datasets that ensure broad conceptual coverage and robust training through dual expansion, a three-dimensional difficulty space, and seven progressive variants per problem; (3) MathBook-RL: a two-stage RL framework including Cold-Start Fine-Tuning to align models with knowledge-oriented chain-of-thought reasoning, and Progressive Alignment RL leveraging average-reward learning with dynamic data scheduling for progressive difficulty alignment; (4) MathBookEval: a benchmark covering all 491 knowledge points with diverse reasoning step distributions. Experimental results show that MathBook-RL achieves competitive performance on four widely used benchmarks and demonstrates strong results on MathBookEval, suggesting promising generalization in mathematical reasoning.