WARM: A Weakly (+Semi) Supervised Math Word Problem Solver

Proceedings of the 29th International Conference on Computational Linguistics, pages 4753–4764 October 12–17, 2022. 4753 WARM: A Weakly (+Semi) Supervised Math Word Problem Solver Oishik Chatterjee ∗ Flipkart Bangalore India Isha Pandey Department of CSE IIT Bombay {oishik75, iishapandey77, aashishwaikar}@gmail.com Aashish Waikar∗ Quadeye Gurgaon India Vishwajeet Kumar IBM India Research Lab Bangalore India vishk024@in.ibm.com Ganesh Ramakrishnan Department of CSE IIT Bombay ganesh@cse.iitb.ac.in Abstract Solving math word problems (MWPs) is an important and challenging problem in natural language processing. Existing approaches to solve MWPs require full supervision in the form of intermediate equations. However, labeling every MWP with its corresponding equations is a time-consuming and expensive task. In order to address this challenge of equa- tion annotation, we propose a weakly super- vised model for solving MWPs by requiring only the final answer as supervision. We ap- proach this problem by first learning to gen- erate the equation using the problem descrip- tion and the final answer, which we subse- quently use to train a supervised MWP solver. We propose and compare various weakly su- pervised techniques to learn to generate equa- tions directly from the problem description and answer. Through extensive experiments, we demonstrate that without using equations for supervision, our approach achieves accu- racy gains of 4.5% and 32% over the state- of-the-art weakly supervised approach (Hong et al., 2021), on the standard Math23K (Wang et al., 2017) and AllArith (Roy and Roth, 2017) datasets respectively. Additionally, we cu- rate and release new datasets of roughly 10k MWPs each in English and in Hindi (a low resource language). These datasets are suit- able for training weakly supervised models. We also present an extension of Warm1 to semi-supervised learning and present further improvements on results, along with insights. 1 Introduction A Math Word Problem (MWP) is a numerical prob- lem expressed in natural language (problem de- bay∗ The author contributed to this work while at IIT Bom- 1Warm stands for WeAkly supeRvised Math solver. scription), that can be transformed into an equa- tion (solution expression), which can be solved to obtain the final answer. In Table 1, we present an example MWP. Automatically solving MWPs has recently gained lot of research interest in nat- ural language processing (NLP). The task of auto- matically solving MWPs is challenging owing to two primary reasons: i) The unavailability of large training datasets with problem descriptions, equa- tions as well as corresponding answers – as de- picted in Table 1, equations can provide full super- vision, since equations can be solved to obtain the answer, and the answer itself amounts to weak su- pervision only; ii) Challenges in parsing the prob- lem description and representing it suitably for ef- fective decoding of the equations. Paucity of com- pletely supervised training data can pose a severe challenge in training MWP solvers. Most exist- ing approaches assume the availability of full su- pervision in the form of both intermediate equa- tions and answers for training. However, anno- tating MWPs with equations is an expensive and time …

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