Analogical Math Word Problems Solving with Enhanced Problem-Solution Association

Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 9454 - 9464 December 7-11, 2022 ©2022 Association for Computational Linguistics Analogical Math Word Problems Solving with Enhanced Problem-Solution Association Zhenwen Liang1, Jipeng Zhang2, and Xiangliang Zhang�1 1University of Notre Dame, {zliang6, xzhang33}@nd.edu 2Hong Kong University of Science and Technology, jzhanggr@conect.ust.hk Abstract Math word problem (MWP) solving is an im- portant task in question answering which re- quires human-like reasoning ability. Analogi- cal reasoning has long been used in mathemat- ical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver’s generalization ability across dif- ferent kinds of MWPs. The key idea, named analogy identification, is to associate the ana- logical MWP pairs in a latent space, i.e., encod- ing an MWP close to another analogical MWP, while moving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between the representations of MWPs and their true solutions. The evalua- tion results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the- art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs. 1 Introduction Math word problem (MWP) solving has attracted considerable attention in recent years. Currently, MWP solver design focuses on generating an equa- tion towards an unknown quantity, with an input problem description, as shown in Figure 1. Build- ing such a successful solver is quite challenging, as it requires mathematical understanding and multi- step reasoning abilities to transform the implied logic behind the problem into a mathematical equa- tion composed of operators and quantities. With the emergence of deep learning, MWP has been effectively studied by Seq2Seq models (Xie and Sun, 2019; Zhang et al., 2020b) and pre-trained language models (PLMs) (Tan et al., 2021; Li et al., Problem 2: Li has $10 to buy some stationery. He has spent $4 to buy pencils, and the rest of the money buys exercise books at $2 each. How many exercise books can he buy? Solution: (10-4)/2 Problem 3: Ming has $10 to buy some stationery. He buys 4 pencils at $0.5 each and 2 books at $1 each. He wants to use the rest of the money to buy pens at $2 each, how many pens can he buy? Solution: (10-4*0.5-2*1)/2 Problem 1: A rope is 24 meters long, we cut 12 meters to make a long jump rope, and use the rest of ropes to make a short jump ropes with a length of 4 meters. How many short jump ropes can be made? Solution: (24-12)/4 Available Resource: 24m Used Resource: 12m Target: 4m ×? Available Resource: $10 Used Resource: $4 Target: $2 ×? Available Resource: $10 Used …

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