Deep learning for symbolic mathematics
Guillaume Lample Facebook AI Research、François Charton Facebook AI Research Equal contribution.
Abstract
Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.
中文速览
神经网络一向被认为擅长统计与模式识别，而非符号计算，但这篇论文挑战了这一刻板印象，专注于让神经网络完成符号积分（symbolic integration）和常微分方程（ordinary differential equations, ODE）求解这两类数学难题。研究者将数学表达式表示为前缀序列（prefix notation），并设计了三种数据生成策略——正向生成、反向生成以及利用分部积分的混合方法——从而构建出数百万规模的带标注训练集，再用序列到序列（sequence-to-sequence）模型进行有监督训练。最终，该模型在积分和微分方程求解任务上的准确率超过了 Matlab 和 Mathematica 等商业计算机代数系统。这一结果表明，只要训练数据设计得当，神经网络有能力掌握高度结构化的符号推理任务，为将深度学习引入形式数学领域开辟了新的思路。
原文 arXiv:1912.01412;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1912.01412v1