Math word problem (MWP) solving faces a dilemma in number representation learning. In order to avoid the number representation issue and reduce the search space of feasible solutions, existing works striving for MWP solving usually replace real numbers with symbolic placeholders to focus on logic reasoning. However, different from common symbolic reasoning tasks like program synthesis and knowledge graph reasoning, MWP solving has extra requirements in numerical reasoning. In other words, instead of the number value itself, it is the reusable numerical property that matters more in numerical reasoning. Therefore, we argue that injecting numerical properties into symbolic placeholders with contextualized representation learning schema can provide a way out of the dilemma in the number representation issue here. In this work, we introduce this idea to the popular pre-training language model (PLM) techniques and build MWP-BERT, an effective contextual number representation PLM. We demonstrate the effectiveness of our MWP-BERT on MWP solving and several MWP-specific understanding tasks on both English and Chinese benchmarks.
翻译:数学字问题(MWP)的解决在数字代表性学习中面临一个难题。为了避免数字代表性问题,减少寻找可行解决办法的空间,现有努力解决数学字的问题通常用象征性的占位符取代实际数字,以逻辑推理为重点。然而,与通用的象征性推理任务不同,如方案合成和知识图推理,解决数学字词问题在数字推理方面有额外要求。换句话说,数字价值本身,在数字推理中更需要的是可重复使用的数字属性。因此,我们认为,将数字属性注入具有背景化代表性学习模式的象征性占位符可提供摆脱此处数字代表性问题的两难处。在这项工作中,我们将这一理念引入通用的培训前语言模式(PLM)技术,并构建一个有效的背景数字PLM。我们展示了我们的MWP-BERT在调解中的有效性,以及在英语和中国基准上几个具体理解MWP的任务。