Tree-structured Decoding for Solving Math Word Problems

By Qianying Liu, Wenyv Guan, Sujian Li, Daisuke Kawahara. 2019

105 citations recorded by the source corpus.

Automatically solving math word problems is an interesting research topic that needs to bridge natural language descriptions and formal math equations. Previous studies introduced end-to-end neural network methods, but these approaches did not efficiently consider an important characteristic of the equation, i.e., an abstract syntax tree. To address this problem, we propose a tree-structured decoding method that generates the abstract syntax tree of the equation in a top-down manner. In addition, our approach can automatically stop during decoding without a redundant stop token. The experimental results show that our method achieves single model state-of-the-art performance on Math23K, which is the largest dataset on this task.

Subfields: Artificial Intelligence, Natural Language Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Xiangliang Zhang
2. Zhenwen Liang
3. Jipeng Zhang
4. Xuanjing Huang
5. Qun Liu
6. Jie Shao
7. Yibin Shen
8. Cheqing Jin

In Natural Language Processing

1. Xiangliang Zhang
2. Zhenwen Liang
3. Jipeng Zhang
4. Jie Shao
5. Yibin Shen
6. Cheqing Jin
7. Lei Wang
8. Xuanjing Huang

Citations in the corpus

• Generate & Rank: A Multi-task Framework for Math Word Problems (2021, positive): “Following Liu et al. (2019a), we also examine the performance of our model in different domains.”
• Graph-to-Tree Learning for Solving Math Word Problems (2020, methodology): “, 2018; Chiang and Chen, 2019) and explicit (Wang et al., 2019; Liu et al., 2019; Xie and Sun, 2019) tree structures.”
• Investigating the Limitations of Transformers with Simple Arithmetic Tasks (2021, background): “Similarly, better numerical skills can be achieved by augmenting input texts with pre-computed numerical computations (Andor et al., 2019) or by explicitly inferring mathematical equations from natural language text (Zou & Lu, 2019a;b; Li et al., 2019; Liu et al., 2019; Shi, 2020).”
• Math Word Problem Solving with Explicit Numerical Values (2021, methodology): “The experimental results provide the following observations: 1) The methods with a tree-structured decoder (Tree-Decoder, GTS, KA-S2T) perform better than methods with a sequence-structured decoder (DNS, S2S).”
• A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving (2020, methodology): “We call this method “ Tree-Decoder ”.”
• A Weakly Supervised Model for Solving Math word Problems (2021, methodology): “More recently, neural network-based MWP solving methods (Wang et al., 2017, 2018a,b; Huang et al., 2018; Chiang and Chen, 2019; Wang et al., 2019; Liu et al., 2019; Xie and Sun, 2019) have been proposed.”
• TM-generation model: a template-based method for automatically solving mathematical word problems (2021, methodology): “The state-of-the-art performance of using the recursive tree structure and simple sequences was 69.0% accuracy [6] and 66.9% [7] in Math23k, respectively.”
• Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems (2020, unknown): “Acc DNS (Wang et al., 2017) 64.7 StackDecoder (Chiang and Chen, 2018) 65.8 Seq2SeqET (Wang et al., 2018) 66.7* T-RNN (Wang et al., 2019) 66.9* Group Attention (Li et al., 2019) 66.9 TreeDecoder (Liu et al., 2019) 69.5 GTS-model (Xie and Sun, 2019) 74.3 Our Approach 77.5 Table 6: The performance of m”
• 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).”
• Teacher-Student Networks with Multiple Decoders for Solving Math Word Problem (2020, methodology): “It has been an interesting natural language understanding task for more than a half decade [Bobrow, 1964] and attracted much attention in recent years [Koncel-Kedziorski et al. , 2015; Shi et al. , 2015; Huang et al. , 2017; Wang et al. , 2018b; Liu et al. , 2019; Xie and Sun, 2019].”
• Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, methodology): “AST-Dec (Liu et al., 2019) used TreeLSTM to realize top-down decoding process.”
• MWP-BERT: A Strong Baseline for Math Word Problems (2021, methodology): “…has been formulated as a pipeline of translating language descriptions to mathematical equations with neural network based encoder-decoder framework (Wang et al., 2018, 2019; Chiang and Chen, 2018; Liu et al., 2019; Li et al., 2019; Xie and Sun, 2019; Zhang et al., 2020b; Shen and Jin, 2020).”
• Solving Math Word Problems with Teacher Supervision (2021, methodology): “On the other hand, the decoder in Seq2Seq is popularly constructed as tree-based math expression generators [Wang et al. , 2018; Liu et al. , 2019].”
• Investigating the Limitations of the Transformers with Simple Arithmetic Tasks (2021, unknown): “Similarly, better numerical skills can be achieved by augmenting input texts with pre-computed numerical computations (Andor et al., 2019) or by explicitly inferring mathematical equations from natural language text (Zou & Lu, 2019a;b; Li et al., 2019; Liu et al., 2019; Shi, 2020).”