This paper introduces the novel task of scoring paraphrases for Algebraic
Word Problems (AWP) and presents a self-supervised method for doing so. In the
current online pedagogical setting, paraphrasing these problems is helpful for
academicians to generate multiple syntactically diverse questions for
assessments. It also helps induce variation to ensure that the student has
understood the problem instead of just memorizing it or using unfair means to
solve it. The current state-of-the-art paraphrase generation models often
cannot effectively paraphrase word problems, losing a critical piece of
information (such as numbers or units) which renders the question unsolvable.
There is a need for paraphrase scoring methods in the context of AWP to enable
the training of good paraphrasers. Thus, we propose ParaQD, a self-supervised
paraphrase quality detection method using novel data augmentations that can
learn latent representations to separate a high-quality paraphrase of an
algebraic question from a poor one by a wide margin. Through extensive
experimentation, we demonstrate that our method outperforms existing
state-of-the-art self-supervised methods by up to 32% while also demonstrating
impressive zero-shot performance.

本文介绍了 ParaQD，采用自监督方法对 Algebraic Word Problems 中的释义进行评分，从而训练良好的释义生成模型，与现有自监督方法相比，ParaQD 的性能提高了 32%。

代数式单词问题的自监督释义质量检测：'John ate 5 apples' != 'John ate some apples

'John ate 5 apples' != 'John ate some apples': Self-Supervised Paraphrase Quality Detection for Algebraic Word Problems

In this paper, we propose a pipeline to convert grade school level algebraic
word problem into program of a formal languageA-IMP. Using natural language
processing tools, we break the problem into sentence fragments which can then
be reduced to functions. The functions are categorized by the head verb of the
sentence and its structure, as defined by (Hosseini et al., 2014). We define
the function signature and extract its arguments from the text using dependency
parsing. We have a working implementation of the entire pipeline which can be
found on our github repository.

本文提出了一种将小学代数单词问题转化为正式语言 A-IMP 的程序的流程，使用自然语言处理工具将问题分解成句子片段，然后按照头动词和句子结构将函数分类，在文本中提取函数签名和参数，使用依赖解析，取得了整个流程的可用实现。

从代数语言问题到程序：一种规范化方法

From Algebraic Word Problem to Program: A Formalized Approach

Solving mathematical word problems (MWPs) automatically is challenging,
primarily due to the semantic gap between human-readable words and
machine-understandable logics. Despite the long history dated back to the1960s,
MWPs have regained intensive attention in the past few years with the
advancement of Artificial Intelligence (AI). Solving MWPs successfully is
considered as a milestone towards general AI. Many systems have claimed
promising results in self-crafted and small-scale datasets. However, when
applied on large and diverse datasets, none of the proposed methods in the
literature achieves high precision, revealing that current MWP solvers still
have much room for improvement. This motivated us to present a comprehensive
survey to deliver a clear and complete picture of automatic math problem
solvers. In this survey, we emphasize on algebraic word problems, summarize
their extracted features and proposed techniques to bridge the semantic gap and
compare their performance in the publicly accessible datasets. We also cover
automatic solvers for other types of math problems such as geometric problems
that require the understanding of diagrams. Finally, we identify several
emerging research directions for the readers with interests in MWPs.

该研究探讨了自动解决数学问题的挑战，包括语言和逻辑之间的语义鸿沟，综述了将人工智能用于代数和几何问题的主要技术及其性能，并探讨未来的研究方向。

语义解析的瓶颈：自动数学题解决方案的调查

The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem  Solvers

Solving algebraic word problems requires executing a series of arithmetic
operations---a program---to obtain a final answer. However, since programs can
be arbitrarily complicated, inducing them directly from question-answer pairs
is a formidable challenge. To make this task more feasible, we solve these
problems by generating answer rationales, sequences of natural language and
human-readable mathematical expressions that derive the final answer through a
series of small steps. Although rationales do not explicitly specify programs,
they provide a scaffolding for their structure via intermediate milestones. To
evaluate our approach, we have created a new 100,000-sample dataset of
questions, answers and rationales. Experimental results show that indirect
supervision of program learning via answer rationales is a promising strategy
for inducing arithmetic programs.

通过生成答案原理，我们间接监督程序学习，从而解决代数字问题。