Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities
Keyur Faldu Embibe、Amit Sheth University of South Carolina、Prashant Kikani Embibe、Manas Gaur University of South Carolina、Aditi Avasthi Embibe Correspondence to
Abstract
Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue to be a key line of research in the coming time. We inspect non-neural and neural methods to solve math word problems narrated in a natural language. We also highlight the ability of these methods to be generalizable, mathematically reasonable, interpretable, and explainable. Neural approaches dominate the current state of the art, and we survey them highlighting three strategies to MWP solving: (1) direct answer generation, (2) expression tree generation for inferring answers, and (3) template retrieval for answer computation. Moreover, we discuss technological approaches, review the evolution of intuitive design choices to solve MWPs and examine them for mathematical reasoning ability. We finally identify several gaps that warrant the need for external knowledge and knowledge-infused learning, among several other opportunities in solving MWPs.
中文速览
让机器自动解答数学应用题（Math Word Problems, MWP）长期以来是人工智能面临的核心挑战之一，难点在于需要同时理解自然语言叙述、提取显式与隐式数量关系，并运用数学规则进行推理。这篇综述系统梳理了从早期规则匹配、语义解析、统计机器学习，到当代深度学习的各类解题方法，重点介绍了神经网络方法的三条技术路线：直接生成答案、生成表达式树再求解、以及检索模板后填入数值计算。研究发现，神经方法在准确率上占据主导，但普遍存在可解释性差、推理脆弱、难以泛化到新问题的缺陷，而非神经方法虽然可解释性更强，却受限于小规模训练数据，同样无法实现通用数学推理。综述最终指出，引入外部知识与知识融合学习是突破现有瓶颈的关键方向，对推动人工智能真正具备数学推理能力具有重要参考价值。
原文 arXiv:2111.05364;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2111.05364v1