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. 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.
689e8afda4caabb4320e5cca
Runqi Qiao
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2025-08-19T10:49:59.108Z
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QRQ
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RichardQRQ
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Qiuna Tan
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Peiqing Yang
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2025-08-18T06:58:03.310Z
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Yang Peiqing
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tianlan22
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Yanzi Wang
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Xiaowan Wang
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Enhui Wan
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Sitong Zhou
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Guanting Dong
claimed_verified
2025-08-18T06:58:07.883Z
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KABI
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dongguanting
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Yuchen Zeng
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Yida Xu
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Jie Wang
689e8afda4caabb4320e5cd5
Chong Sun
689e8afda4caabb4320e5cd6
Chen Li
689e8afda4caabb4320e5cd7
Honggang Zhang
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. 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.
We-Math 2.0 enhances MLLMs' mathematical reasoning through a structured knowledge system, model-centric data space modeling, and reinforcement learning, demonstrating competitive performance on benchmarks.
Multimodal Large Language Models MLLMs mathematical reasoning MathBook Knowledge System MathBook-Standard MathBook-Pro MathBook-RL Cold-Start Fine-tuning Progressive Alignment RL MathBookEval chain-of-thought reasoning average-reward learning dynamic data scheduling