In this paper, we propose SCANING, an unsupervised framework for paraphrasing
via controlled noise injection. We focus on the novel task of paraphrasing
algebraic word problems having practical applications in online pedagogy as a
means to reduce plagiarism as well as ensure understanding on the part of the
student instead of rote memorization. This task is more complex than
paraphrasing general-domain corpora due to the difficulty in preserving
critical information for solution consistency of the paraphrased word problem,
managing the increased length of the text and ensuring diversity in the
generated paraphrase. Existing approaches fail to demonstrate adequate
performance on at least one, if not all, of these facets, necessitating the
need for a more comprehensive solution. To this end, we model the noising
search space as a composition of contextual and syntactic aspects and sample
noising functions consisting of either one or both aspects. This allows for
learning a denoising function that operates over both aspects and produces
semantically equivalent and syntactically diverse outputs through grounded
noise injection. The denoising function serves as a foundation for learning a
paraphrasing function which operates solely in the input-paraphrase space
without carrying any direct dependency on noise. We demonstrate SCANING
considerably improves performance in terms of both semantic preservation and
producing diverse paraphrases through extensive automated and manual evaluation
across 4 datasets.

本文提出了 SCANING，这是一个通过受控噪声注入进行释义的无监督框架，它着重于代数单词问题的释义，并进行了广泛的自动化和手动评估，从而提高了语义保存和产生不同释义方面的性能。

通过噪声实现连贯性和多样性：基于结构感知去噪的自监督释义生成

Coherence and Diversity through Noise: Self-Supervised Paraphrase Generation via Structure-Aware Denoising

The paper discusses the capacities and limitations of current artificial
intelligence (AI) technology to solve word problems that combine elementary
knowledge with commonsense reasoning. No existing AI systems can solve these
reliably. We review three approaches that have been developed, using AI natural
language technology: outputting the answer directly, outputting a computer
program that solves the problem, and outputting a formalized representation
that can be input to an automated theorem verifier. We review some benchmarks
that have been developed to evaluate these systems and some experimental
studies. We discuss the limitations of the existing technology at solving these
kinds of problems. We argue that it is not clear whether these kinds of
limitations will be important in developing AI technology for pure mathematical
research, but that they will be important in applications of mathematics, and
may well be important in developing programs capable of reading and
understanding mathematical content written by humans.

本文讨论了当前人工智能技术在解决结合基本知识和常识推理的词问题方面的能力和局限性。我们回顾了三种方法，并讨论了现有技术在解决这些问题方面的限制。我们认为，这些限制可能对数学应用和人类书写的数学内容的理解有重要影响。

数学、应用题、常识和人工智能

Mathematics, word problems, common sense, and artificial intelligence

Math word problems form a natural abstraction to a range of quantitative
reasoning problems, such as understanding financial news, sports results, and
casualties of war. Solving such problems requires the understanding of several
mathematical concepts such as dimensional analysis, subset relationships, etc.
In this paper, we develop declarative rules which govern the translation of
natural language description of these concepts to math expressions. We then
present a framework for incorporating such declarative knowledge into word
problem solving. Our method learns to map arithmetic word problem text to math
expressions, by learning to select the relevant declarative knowledge for each
operation of the solution expression. This provides a way to handle multiple
concepts in the same problem while, at the same time, support interpretability
of the answer expression. Our method models the mapping to declarative
knowledge as a latent variable, thus removing the need for expensive
annotations. Experimental evaluation suggests that our domain knowledge based
solver outperforms all other systems, and that it generalizes better in the
realistic case where the training data it is exposed to is biased in a
different way than the test data.

本文探讨了将自然语言描述的概念转换成数学表达式的声明性规则，并提出了一种将此类声明性知识纳入解决数学问题的框架。通过学习如何选择与解决方案表达式的每个操作相关的声明性知识，实现了将算术单词问题文本映射到数学表达式，同时支持答案表达式的可解释性。实验评估表明，基于领域知识的求解器优于其他所有系统，并且在训练数据与测试数据偏向不同的实际情况下更具有普适性。