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A Numeracy-Enhanced Decoding forĀ Solving Math Word Problem

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Natural Language Processing and Chinese Computing (NLPCC 2023)

Abstract

Deep neural models have achieved promising progress in solving Math Word Problems (MWPs) recently. This paper presents a deep neural solver by adopting numeracy-enhanced decoding to promote the performance of expressions generation. It leverages numerical properties to enhance the capabilities of the decoder, primarily focusing on two aspects: token embedding and target prediction. For token embedding, this paper proposes a numeracy-enhanced token embedding method, which fuses the explicit numerical feature with the contextual feature for number tokens, enabling the decoder to perceive numerical properties during the inference. For target prediction, this paper proposes a dynamic target prediction method, which utilizes a numerical attention network to identify the mathematical category of the problem and adaptively invokes category-aware parameter matrices to generate diverse expressions for different problems. Experimental results demonstrate that the proposed method not only achieves competitive performance on the Chinese MWP dataset but also achieves state-of-the-art results on the NLPCC Shared Task 3 dataset.

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Change history

  • 29 October 2023

    A correction has been published.

Notes

  1. 1.

    http://tcci.ccf.org.cn/conference/2023/taskdata.php.

References

  1. Amini, A., Gabriel, S., Lin, S., Koncel-Kedziorski, R., Choi, Y., Hajishirzi, H.: MathQA: towards interpretable math word problem solving with operation-based formalisms. In: Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pp. 2357ā€“2367 (2019)

    Google ScholarĀ 

  2. Bobrow, D.G.: A question-answering system for high school algebra word problems. In: Proceedings of the 1964 Fall Joint Computer Conference, pp. 591ā€“614 (1964)

    Google ScholarĀ 

  3. Cui, Y., Che, W., Liu, T., Qin, B., Yang, Z.: Pre-training with whole word masking for Chinese BERT. IEEE/ACM Trans. Audio Speech Lang. Process. 29, 3504ā€“3514 (2021)

    ArticleĀ  Google ScholarĀ 

  4. Hu, E.J., et al.: LoRA: low-rank adaptation of large language models. arXiv:2106.09685 (2021)

  5. Jie, Z., Li, J., Lu, W.: Learning to reason deductively: math word problem solving as complex relation extraction. In: Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics, pp. 5944ā€“5955 (2022)

    Google ScholarĀ 

  6. Kintsch, W., Greeno, J.G.: Understanding and solving word arithmetic problems. Psychol. Rev. 92, 109 (1985)

    ArticleĀ  Google ScholarĀ 

  7. Kushman, N., Artzi, Y., Zettlemoyer, L., Barzilay, R.: Learning to automatically solve algebra word problems. In: Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics, pp. 271ā€“281 (2014)

    Google ScholarĀ 

  8. Li, Z., et al.: Seeking patterns, not just memorizing procedures: contrastive learning for solving math word problems. In: Findings of the Association for Computational Linguistics, NAACL 2022, pp. 2486ā€“2496 (2022)

    Google ScholarĀ 

  9. Liang, Z., et al.: MWP-BERT: numeracy-augmented pre-training for math word problem solving. In: Findings of the Association for Computational Linguistics, NAACL 2022, pp. 997ā€“1009 (2022)

    Google ScholarĀ 

  10. Liang, Z., Zhang, J., Zhang, X.: Analogical math word problems solving with enhanced problem-solution association. arXiv:2212.00837 (2022)

  11. Lin, X., et al.: Learning relation-enhanced hierarchical solver for math word problems. IEEE Trans. Neural Netw. Learn. Syst. (2023, early access)

    Google ScholarĀ 

  12. Lin, X., et al.: HMS: a hierarchical solver with dependency-enhanced understanding for math word problem. In: Proceedings of the 35th AAAI Conference on Artificial Intelligence, pp. 4232ā€“4240 (2021)

    Google ScholarĀ 

  13. Liu, Q., Guan, W., Li, S., Kawahara, D.: Tree-structured decoding for solving math word problems. In: Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing, pp. 2370ā€“2379 (2019)

    Google ScholarĀ 

  14. Mor, G., Ankit, G., Jonathan, B.: Injecting numerical reasoning skills into language models. In: Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pp. 946ā€“958 (2020)

    Google ScholarĀ 

  15. Raffel, C., et al.: Exploring the limits of transfer learning with a unified text-to-text transformer. J. Mach. Learn. Res. 21, 5485ā€“5551 (2020)

    MathSciNetĀ  Google ScholarĀ 

  16. Roy, S., Roth, D.: Unit dependency graph and its application to arithmetic word problem solving. In: Proceedings of the 31st AAAI Conference on Artificial Intelligence, pp. 3082ā€“3088 (2017)

    Google ScholarĀ 

  17. Shen, J., et al.: Generate & rank: a multi-task framework for math word problems. In: Findings of the Association for Computational Linguistics, EMNLP 2021, pp. 2269ā€“2279 (2021)

    Google ScholarĀ 

  18. Shi, S., Wang, Y., Lin, C.Y., Liu, X., Rui, Y.: Automatically solving number word problems by semantic parsing and reasoning. In: Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pp. 1132ā€“1142 (2015)

    Google ScholarĀ 

  19. Touvron, H., et al.: LLaMA: open and efficient foundation language models. arXiv arXiv:2302.13971 (2023)

  20. Wang, L., Wang, Y., Cai, D., Zhang, D., Liu, X.: Translating a math word problem to an expression tree. In: Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 1064ā€“1069 (2018)

    Google ScholarĀ 

  21. Wang, Y., Liu, X., Shi, S.: Deep neural solver for math word problems. In: Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pp. 845ā€“854 (2017)

    Google ScholarĀ 

  22. Wu, Q., Zhang, Q., Wei, Z.: An edge-enhanced hierarchical graph-to-tree network for math word problem solving. In: Findings of the Association for Computational Linguistics, EMNLP 2021, pp. 1473ā€“1482 (2021)

    Google ScholarĀ 

  23. Xie, Z., Sun, S.: A goal-driven tree-structured neural model for math word problems. In: Proceedings of the 28th International Joint Conference on Artificial Intelligence, pp. 5299ā€“5305 (2019)

    Google ScholarĀ 

  24. Yu, X., Wang, M., Gan, W., He, B., Ye, N.: A framework for solving explicit arithmetic word problems and proving plane geometry theorems. Int. J. Pattern Recognit. Artif. Intell. 33, 1940005:1ā€“1940005:21 (2019)

    Google ScholarĀ 

  25. Zhang, J., et al.: Teacher-student networks with multiple decoders for solving math word problem. In: Proceedings of the 29th International Joint Conference on Artificial Intelligence, pp. 4011ā€“4017 (2020)

    Google ScholarĀ 

  26. Zhang, J., et al.: Graph-to-tree learning for solving math word problems. In: Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pp. 3928ā€“3937 (2020)

    Google ScholarĀ 

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Acknowledgements

This work is partially supported by the General Program of the National Natural Science Foundation of China (Grant No: 61977029) and the China Postdoctoral Science Foundation (Grant No: 2023M731245).

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Correspondence to Xinguo Yu .

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Peng, R., Yang, C., Huang, L., Lyu, X., Meng, H., Yu, X. (2023). A Numeracy-Enhanced Decoding forĀ Solving Math Word Problem. In: Liu, F., Duan, N., Xu, Q., Hong, Y. (eds) Natural Language Processing and Chinese Computing. NLPCC 2023. Lecture Notes in Computer Science(), vol 14304. Springer, Cham. https://doi.org/10.1007/978-3-031-44699-3_11

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  • DOI: https://doi.org/10.1007/978-3-031-44699-3_11

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