用形式化验证生成可信几何题数据，提升模型推理能力
TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving
- 通过形式化验证确保逻辑严谨性，生成含图文的多模态几何题
- 合成数据集GeoTrust训练后，模型在多个外分布测试集上表现显著提升
- 适合需要可靠逻辑推理能力的数学智能研究者使用
几何问题求解（GPS）需要精确的多模态理解与严格的逐步逻辑推理。然而，构建具备能力的多模态大语言模型（MLLM）在GPS方面严重受限于高质量、可验证数据的匮乏。现有数据获取范式或存在模态不完整与未验证的逻辑断层（“信念跳跃”），或依赖形式化引擎生成结构单一、僵化的数据，难以产生高难度问题或促进真实的自然语言推理。为此，我们提出TrustGeoGen——一个自主且形式化的几何数据生成引擎。该引擎通过形式化验证严格保证推理可信度，同时生成包含前提、视觉图示与解法的多模态数据。为系统提升问题难度，引入难度感知过滤与迭代自举机制。此外，提出“连接思维”以弥合刚性形式逻辑与流畅人类推理间的语义鸿沟，确保逻辑连贯。还设计GeoExplore系列采样算法，基于不同思维模板提取多样解题路径。大量实验表明，在合成数据集GeoTrust上训练的模型显著增强深层几何推理能力，并在多个分布外（OOD）基准（GeoQA、Geometry3K、OlympiadBench）上取得显著性能提升。
原文摘要 · Abstract (English)
Geometric problem solving (GPS) requires precise multimodal understanding and rigorous, step-by-step logical reasoning. However, developing capable Multimodal Large Language Models (MLLMs) for GPS is heavily bottlenecked by the scarcity of high-quality, verifiable data. Existing data acquisition paradigms either suffer from modality incompleteness and unverified logical gaps ("leaps-of-faith"), or rely on formal engines that generate rigid, structurally homogeneous data, failing to produce high-difficulty problems or foster genuine natural-language reasoning. To overcome these limitations, we introduce TrustGeoGen, an autonomous and formalized geometric data generation engine. TrustGeoGen strictly guarantees reasoning trustworthiness through formal verification while generating multimodally integrated data, including premises, visual diagrams, and solutions. To systematically scale problem difficulty, we incorporates difficulty-aware filtering and iterative bootstrapping mechanism. Furthermore, we propose "connection thinking" to bridge the semantic gap between rigid formal logic and fluent human-like reasoning, ensuring coherent logical transitions. We also introduce the GeoExplore family of sampling algorithms to extract diverse problem-solving trajectories based on various thinking templates. Extensive experiments demonstrate that training models on our synthesized dataset, GeoTrust, substantially enhances deep geometric reasoning capabilities and yields significant performance gains across out-of-distribution (OOD) benchmarks, including GeoQA, Geometry3K, and OlympiadBench.Our code and data can be found at https://github.com/InternScience/TrustGeoGen
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