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

arXiv: https://arxiv.org/abs/2508.10433 · HTML: https://mlsanity.com/paper/2508.10433/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 55 of its 77 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 55)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (2023)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suites](https://mlsanity.com/paper/2404.16821/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning](https://mlsanity.com/paper/2507.01006/) (2025)
- [DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learning](https://mlsanity.com/paper/2505.14362/) (2025)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Seed1.5-VL Technical Report](https://mlsanity.com/paper/2505.07062/) (2025)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)

## Built on by (most cited first, 30 of 32)

- [LongVT: Incentivizing "Thinking with Long Videos" via Native Tool Calling](https://mlsanity.com/paper/2511.20785/) (2025)
- [Agent-World: Scaling Real-World Environment Synthesis for Evolving General Agent Intelligence](https://mlsanity.com/paper/2604.18292/) (2026)
- [Agentic Entropy-Balanced Policy Optimization](https://mlsanity.com/paper/2510.14545/) (2025)
- [OpenMMReasoner: Pushing the Frontiers for Multimodal Reasoning with an Open and General Recipe](https://mlsanity.com/paper/2511.16334/) (2025)
- [V-Thinker: Interactive Thinking with Images](https://mlsanity.com/paper/2511.04460/) (2025)
- [SpaceVista: All-Scale Visual Spatial Reasoning from mm to km](https://mlsanity.com/paper/2510.09606/) (2025)
- [Toward Effective Tool-Integrated Reasoning via Self-Evolved Preference Learning](https://mlsanity.com/paper/2509.23285/) (2025)
- [PyVision-RL: Forging Open Agentic Vision Models via RL](https://mlsanity.com/paper/2602.20739/) (2026)
- [Thinking with Programming Vision: Towards a Unified View for Thinking with Images](https://mlsanity.com/paper/2512.03746/) (2025)
- [Euclid's Gift: Enhancing Spatial Perception and Reasoning in Vision-Language Models via Geometric Surrogate Tasks](https://mlsanity.com/paper/2509.24473/) (2025)
- [Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decoding](https://mlsanity.com/paper/2603.13366/) (2026)
- [Vero: An Open RL Recipe for General Visual Reasoning](https://mlsanity.com/paper/2604.04917/) (2026)
- [Rethinking Token-Level Policy Optimization for Multimodal Chain-of-Thought](https://mlsanity.com/paper/2603.22847/) (2026)
- [TIM-PRM: Verifying multimodal reasoning with Tool-Integrated PRM](https://mlsanity.com/paper/2511.22998/) (2025)
- [CCCaption: Dual-Reward Reinforcement Learning for Complete and Correct Image Captioning](https://mlsanity.com/paper/2602.21655/) (2026)
- [Credit Where It is Due: Cross-Modality Connectivity Drives Precise Reinforcement Learning for MLLM Reasoning](https://mlsanity.com/paper/2602.11455/) (2026)
- [DeepVision-103K: A Visually Diverse, Broad-Coverage, and Verifiable Mathematical Dataset for Multimodal Reasoning](https://mlsanity.com/paper/2602.16742/) (2026)
- [Learning When to Look: A Disentangled Curriculum for Strategic Perception in Multimodal Reasoning](https://mlsanity.com/paper/2512.17227/) (2025)
- [CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving](https://mlsanity.com/paper/2601.01874/) (2026)
- [ET-Agent: Incentivizing Effective Tool-Integrated Reasoning Agent via Behavior Calibration](https://mlsanity.com/paper/2601.06860/) (2026)
- [RetouchIQ: MLLM Agents for Instruction-Based Image Retouching with Generalist Reward](https://mlsanity.com/paper/2602.17558/) (2026)
- [Persistent Visual Memory: Sustaining Perception for Deep Generation in LVLMs](https://mlsanity.com/paper/2605.00814/) (2026)
- [LiveK12Bench: Have Large Multimodal Models Truly Conquered High School-level Examinations?](https://mlsanity.com/paper/2605.26781/) (2026)
- [Bypassing Copyright Protection in Diffusion-based Customization via Two-Stage Latent Feature Optimization](https://mlsanity.com/paper/2606.09909/) (2026)
- [RL Forgets! Towards Continual Policy Optimization](https://mlsanity.com/paper/2607.04364/) (2026)
- [AnE: Pushing the Reasoning Frontier of Multimodal LLMs via Anchor Evolution](https://mlsanity.com/paper/2605.25571/) (2026)
- [MMVistaReason: Toward Open-Data and Post-Training Recipes for Multimodal Reasoning](https://mlsanity.com/paper/2610.01352/) (2026)
- [Towards Mixed-Modal Retrieval for Universal Retrieval-Augmented Generation](https://mlsanity.com/paper/2510.17354/) (2025)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [VeriEvol: Scaling Multimodal Mathematical Reasoning via Verifiable Evol-Instruct](https://mlsanity.com/paper/2606.23543/) (2026)

## Abstract (arXiv)

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.