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.

研究了解决自然语言描述的数学问题的非神经和神经方法，并突出了这些方法具有可泛化、数学合理、可解释和可解释的能力，提出使用外部知识和知识渗透学习的需求和机会。

走向可行的数学推理：解决数学应用题的挑战、策略和机遇

Towards Tractable Mathematical Reasoning: Challenges, Strategies, and  Opportunities for Solving Math Word Problems

The recent series of innovations in deep learning (DL) have shown enormous
potential to impact individuals and society, both positively and negatively.
The DL models utilizing massive computing power and enormous datasets have
significantly outperformed prior historical benchmarks on increasingly
difficult, well-defined research tasks across technology domains such as
computer vision, natural language processing, signal processing, and
human-computer interactions. However, the Black-Box nature of DL models and
their over-reliance on massive amounts of data condensed into labels and dense
representations poses challenges for interpretability and explainability of the
system. Furthermore, DLs have not yet been proven in their ability to
effectively utilize relevant domain knowledge and experience critical to human
understanding. This aspect is missing in early data-focused approaches and
necessitated knowledge-infused learning and other strategies to incorporate
computational knowledge. This article demonstrates how knowledge, provided as a
knowledge graph, is incorporated into DL methods using knowledge-infused
learning, which is one of the strategies. We then discuss how this makes a
fundamental difference in the interpretability and explainability of current
approaches, and illustrate it with examples from natural language processing
for healthcare and education applications.

该论文展示了知识图谱注入的深度学习方法，并讨论了这种方法对当前自然语言处理在医疗和教育领域中的可解释性和可解释性的基本差异。