以簡化法處理數學文字題

A Reduction Based Approach for Math Word Problem

黃孟霖(Meng-Lin Huang)

指導教授 ： 項傑

國立臺灣大學/電機資訊學院/資訊工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202002823

摘要

數學文字題包含自然語言理解與邏輯推斷，所以一直以來都被視為人工智慧領域重要的應用，其中小學數學問題並沒有複雜的數學計算與文字敘述，研究人員能讓其設計出來的系統專注於語言理解與邏輯推斷的部分，而不需要涵蓋廣大的文法以及數學相關的Domain Knowledge，也因此非常適合用來當作衡量的數據集。
本篇論文提出一個新的小學數學解題系統，與現今其他以神經網路建構的系統的不同之處在於此系統著重於邏輯推斷過程。我們的系統除了可以算出答案以外還能產生生出此答案的解釋，並且透過簡化題目來減少所需要設計的規則。此外針對此系統目前處理不了的問題我們也做了錯誤分析，並設計了新的句子簡化方法，更進一步的將其與系統進行結合，最終此系統在我們提出的小學數學數據集上得到顯著的成果。

關鍵字

數學文字問題 ； 自然語言理解 ； 句子過濾 ； 邏輯推斷 ； 深度學習

並列摘要

Math Word Problem involves natural language understanding and logical inference, thus it has been regarded as a major application of AI. Because there is no complicated mathematical calculation in elementary math word problem, researchers could concentrate on the task of understanding and inference.

In this thesis, we propose a novel elementary math solver system, named “elementary mathematics problem solver”. The difference between prevailing neural network based systems and ours is that we focus more on the process of logical inference and domain common sense. Our solver not only answers the question, but also gives corresponding explanations. We adopt label sequence as “pattern” to identify similar sentences and problems. Solution strategy is described in natural language script so that teachers can make change at will. We greatly reduce the patterns needed by filtering out non-essential words in problem sentences. Since the explanations are written in natural language, error analysis is very intuitive. Our problem solving philosophy is based on mimicking how humans learn to solve a problem. Ultimately, our system achieves significant performance on our elementary mathematics dataset.

並列關鍵字

math word problem ； natural language understanding ； sentence input filtering ； logic inference ； deep learning

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