用神经符号协作解几何题，步骤清晰可读。
AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning
- 先用神经网络理解题意，再用符号推理一步步推导
- 在基准数据集上表现领先，99%的推理步骤逻辑连贯
- 适合需要可解释推理过程的数学教育场景
几何问题求解在人工智能中面临独特挑战，需兼具多模态理解与严谨数学推理能力。现有方法多为神经或符号两类，均存在可靠性与可解释性不足的问题。为此，我们提出AutoGPS，一种神经符号协同框架，通过简洁、可靠且人类可读的推理过程解决几何问题。该框架包含多模态问题形式化器（MPF）和演绎符号推理器（DSR）。MPF利用神经跨模态理解将几何题转化为结构化形式语言表示，并接受DSR反馈优化；DSR将形式化结果作为输入，将问题求解建模为超图扩展任务，执行数学严谨的推导，生成最小且可读性强的分步解答。大量实验表明，AutoGPS在基准数据集上达到顶尖性能。人工分步推理评估进一步验证其卓越的可靠性和可解释性，99%的推理步骤保持逻辑一致。
原文摘要 · Abstract (English)
Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories: neural-based and symbolic-based methods, both of which exhibit limitations in reliability and interpretability. To address this challenge, we propose AutoGPS, a neuro-symbolic collaborative framework that solves geometry problems with concise, reliable, and human-interpretable reasoning processes. Specifically, AutoGPS employs a Multimodal Problem Formalizer (MPF) and a Deductive Symbolic Reasoner (DSR). The MPF utilizes neural cross-modal comprehension to translate geometry problems into structured formal language representations, with feedback from DSR collaboratively. The DSR takes the formalization as input and formulates geometry problem solving as a hypergraph expansion task, executing mathematically rigorous and reliable derivation to produce minimal and human-readable stepwise solutions. Extensive experimental evaluations demonstrate that AutoGPS achieves state-of-the-art performance on benchmark datasets. Furthermore, human stepwise-reasoning evaluation confirms AutoGPS's impressive reliability and interpretability, with 99\% stepwise logical coherence.
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