A Goal-Driven Tree-Structured Neural Model for Math Word Problems

By Zhipeng Xie, Shichao Sun. 2019

242 citations recorded by the source corpus.

Most existing neural models for math word problems exploit Seq2Seq model to generate solution expressions sequentially from left to right, whose results are far from satisfactory due to the lack of goal-driven mechanism commonly seen in human problem solving. This paper proposes a tree-structured neural model to generate expression tree in a goal-driven manner. Given a math word problem, the model first identifies and encodes its goal to achieve, and then the goal gets decomposed into sub-goals combined by an operator in a top-down recursive way. The whole process is repeated until the goal is simple enough to be realized by a known quantity as leaf node. During the process, two-layer gated-feedforward networks are designed to implement each step of goal decomposition, and a recursive neural network is used to encode fulfilled subtrees into subtree embeddings, which provides a better representation of subtrees than the simple goals of subtrees. Experimental results on the dataset Math23K have shown that our tree-structured model outperforms significantly several state-of-the-art models.

Subfields: Artificial Intelligence, Information Systems, Natural Language Processing

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Citations in the corpus

Training Verifiers to Solve Math Word Problems (2021, methodology): “More recent work has improved performance by designing specialized encoder-decoder architectures (Amini et al., 2019; Chiang and Chen, 2018; Xie and Sun, 2019; Chen et al., 2020; Li et al., 2020), with the strongest results often relying on large pretrained encoders from the BERT family (Chen et…”
MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers (2021, methodology): “, 2019a) GTS GRU TreeDecoder (Xie and Sun, 2019) SAU-Solver GRU TreeDecoder (Qin et al.”
Are NLP Models really able to Solve Simple Math Word Problems? (2021, methodology): “GTS (S) (Xie and Sun, 2019) 82.”
Generate & Rank: A Multi-task Framework for Math Word Problems (2021, neutral): “…studies formalize MWP as a generation task and commonly adopt LSTM-based sequence-to-sequence (Seq2Seq) models (Wang et al., 2017, 2018b; Xie and Sun, 2019), where problem texts are source sequences, mathematical expressions are target sequences and the model learns the mapping Original MWP…”
Graph-to-Tree Learning for Solving Math Word Problems (2020, methodology): “Other models (Wang et al., 2019; Liu et al., 2019; Xie and Sun, 2019) have generated an expression tree explicitly to derive the final answer.”
Distilling Multi-Step Reasoning Capabilities of Large Language Models into Smaller Models via Semantic Decompositions (2022, background): “Solving MWPs has been an interesting area of research for the last couple of years (Kushman et al., 2014; Hosseini et al., 2014; Roy et al., 2015; Seo et al., 2015; Sachan and Xing, 2017; Amini et al., 2019; Xie and Sun, 2019; Zhang et al., 2020).”
Solving Math Word Problems with Teacher Supervision (2021, methodology): “Following the state-of-the-art MWP solver GTS model [Xie and Sun, 2019], we employ a bidirectional Gated Recurrent Unit (GRU) [Cho et al. , 2014] as our encoder for learning the MWP representation.”
Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems (2020, methodology): “…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 models on Math23K.”
Neural Mathematical Solver with Enhanced Formula Structure (2020, methodology): “Along this line, research works have attempted many methods, such as statistical learning [7], and deep learning models [13].”
Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, methodology): “Following prior works (Wang et al., 2017; Chiang and Chen, 2019; Xie and Sun, 2019), we conduct 5fold cross-validation on Math23K.”
Investigating Math Word Problems using Pretrained Multilingual Language Models (2021, unknown): “, 2015) and generation-based methods (Wang et al., 2018; Xie and Sun, 2019).”
Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems (2021, unknown): “GTS 3 (Xie and Sun, 2019) trees through a tree structure decoder in a goal-driven mannner.”
Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, methodology): “Since GTS doesn’t integrate the numerical comparison information in the model, it cannot deal with these expressions well.”
HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem (2021, methodology): “To investigate the performance of our model with the increasing length of expressions and problems, we report the number of test instances over different expression and problem lengths in Table 3 and 4, and the accuracies of corresponding test instances compared with the GTS model in Figure 4 and 5 ”
Teacher-Student Networks with Multiple Decoders for Solving Math Word Problem (2020, methodology): “The solution expression is represented by either a sequential [ Wang et al. , 2017; Wang et al. , 2018a; Chiang and Chen, 2019] or a tree structure [Liu et al. , 2019; Xie and Sun, 2019].”
GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning (2021, unknown): “…including traditional machine learning approaches (Kushman et al., 2014; Zhou et al., 2015; Huang et al., 2016) and network-based models (Wang et al., 2017, 2018; Xie and Sun, 2019), while solving geometric problems has been rarely investigated (Seo et al., 2014, 2015a; Sachan et al., 2017).”