Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks
By Jinghui Qin, Xiaodan Liang, Yining Hong, Jianheng Tang, Liang Lin. 2021
71 citations recorded by the source corpus.
Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver (NS-Solver) to explicitly and seamlessly incorporate different levels of symbolic constraints by auxiliary tasks. Our NS-Solver consists of a problem reader to encode problems, a programmer to generate symbolic equations, and a symbolic executor to obtain answers. Along with target expression supervision, our solver is also optimized via 4 new auxiliary objectives to enforce different symbolic reasoning: a) self-supervised number prediction task predicting both number quantity and number locations; b) commonsense constant prediction task predicting what prior knowledge (e.g. how many legs a chicken has) is required; c) program consistency checker computing the semantic loss between predicted equation and target equation to ensure reasonable equation mapping; d) duality exploiting task exploiting the quasi-duality between symbolic equation generation and problem’s part-of-speech generation to enhance the understanding ability of a solver. Besides, to provide a more realistic and challenging benchmark for developing a universal and scalable solver, we also construct a new largescale MWP benchmark CM17K consisting of 4 kinds of MWPs (arithmetic, one-unknown linear, one-unknown non-linear, equation set) with more than 17K samples. Extensive experiments on Math23K and our CM17k demonstrate the superiority of our NS-Solver compared to state-of-the-art methods.
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Natural Language Processing
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Citations in the corpus
- MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers (2021, methodology): “…MWP solving methods have been proposed, including graph neural networks based (Li et al., 2020), template based (Lee et al., 2021), neural symbolic (Qin et al., 2021), pre-trained based (Liang et al., 2021), multilingual pre-trained based methods (Tan et al., 2021), and solvers using external…”
- Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, background): “GroupAttn (Li et al., 2019) 69.5 66.9 mBERT-LSTM (Tan et al., 2021) 75.1 - BERT-BERT (Lan et al., 2021) - 76.6 Roberta-Roberta (Lan et al., 2021) - 76.9 S 2 T / G 2 T GTS (Xie and Sun, 2019) 75.6 74.3 KA-S2T† (Wu et al., 2020) 76.3 - MultiE&D (Shen and Jin, 2020) 78.4 76.9 Graph2Tree (Zhang et al., ”
- Large Language Models for Mathematical Reasoning: Progresses and Challenges (2024, background): “…(Roy and Roth, 2015) 600 E Multi-step reasoning D RAW -1K (Upadhyay and Chang, 2017) 1K E M ATH 23K (Wang et al., 2017) 23K E Chinese A PE 210K (Zhao et al., 2020) 210K E Chinese K6 (Yang et al., 2023) 600 E Chinese; grade 1-6 CM17K (Qin et al., 2021) 17K M H Chinese; grade 6-12 Q u e s ti on -”
- A Survey of Deep Learning for Mathematical Reasoning (2022, unknown): “Sequence-to-tree (Seq2Tree) models explicitly model the tree structure when encoding the output sequences (Liu et al., 2019a; Xie and Sun, 2019; Wu et al., 2020; Zhang et al., 2020a; Zaporojets et al., 2021; Qin et al., 2021; Wu et al., 2021b; Lin et al., 2021; Hong et al., 2021a).”