用专用语言让程序自动解方程更准更简洁。
MathDSL: A Domain-Specific Language for Concise Mathematical Solutions Via Program Synthesis
- 设计数学求解专用语言MathDSL，结合程序合成生成解法。
- 在解线性方程上准确率与简洁性均优于强化学习方法。
- 生成结果可解释，适合用于数学教育场景。
我们提出MathDSL，一种用于数学方程求解的领域专用语言。当部署于程序合成模型中时，其性能超越现有基于强化学习的方法。我们引入量化指标评估数学解法的简洁性，并证明生成解法质量显著提升。实验表明，使用DreamCoder结合MathDSL求解线性方程，准确率与简洁性均优于强化学习系统。此外，若将先前强化学习系统的动作空间作为语言，MathDSL仍表现更优。DreamCoder通过MathDSL将方程求解策略以可读形式存入程序库，生成的人类可理解解题路径可用于数学教育应用。
原文摘要 · Abstract (English)
We present MathDSL, a Domain-Specific Language (DSL) for mathematical equation solving, which, when deployed in program synthesis models, outperforms state-of-the-art reinforcement-learning-based methods. We also introduce a quantitative metric for measuring the conciseness of a mathematical solution and demonstrate the improvement in the quality of generated solutions compared to other methods. Our system demonstrates that a program synthesis system (DreamCoder) using MathDSL can generate programs that solve linear equations with greater accuracy and conciseness than using reinforcement learning systems. Additionally, we demonstrate that if we use the action spaces of previous reinforcement learning systems as DSLs, MathDSL outperforms the action-space-DSLs. We use DreamCoder to store equation-solving strategies as learned abstractions in its program library and demonstrate that by using MathDSL, these can be converted into human-interpretable solution strategies that could have applications in mathematical education.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。