Template-Based Math Word Problem Solvers with Recursive Neural Networks

By Lei Wang, Dongxiang Zhang, Jipeng Zhang, Xing Xu, Lianli Gao, Bing Tian Dai, Heng Tao Shen. 2019

168 citations recorded by the source corpus.

The design of automatic solvers to arithmetic math word problems has attracted considerable attention in recent years and a large number of datasets and methods have been published. Among them, Math23K is the largest data corpus that is very helpful to evaluate the generality and robustness of a proposed solution. The best performer in Math23K is a seq2seq model based on LSTM to generate the math expression. However, the model suffers from performance degradation in large space of target expressions. In this paper, we propose a template-based solution based on recursive neural network for math expression construction. More specifically, we first apply a seq2seq model to predict a tree-structure template, with inferred numbers as leaf nodes and unknown operators as inner nodes. Then, we design a recursive neural network to encode the quantity with Bi-LSTM and self attention, and infer the unknown operator nodes in a bottom-up manner. The experimental results clearly establish the superiority of our new framework as we improve the accuracy by a wide margin in two of the largest datasets, i.e., from 58.1% to 66.9% in Math23K and from 62.8% to 66.8% in MAWPS.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, 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): “The models include Seq2seq, Seq2tree, Graph2tree, and commonly-used non-pretrained (AttSeq2Seq (Bahdanau et al., 2014), LSTMVAE (Zhang et al., 2016), and Trans-former (Vaswani et al., 2017)) and pretrained models (GPT-2 (Radford et al., 2019), BERTGen (De-vlin et al., 2018), and RoBERTaGen (Liu et a”
Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, methodology): “Other approaches improve the seq2seq model with reinforcement learning (Huang et al., 2018), template-based methods (Wang et al., 2019), and group attention mechanism (Li et al., 2019).”
Generate & Rank: A Multi-task Framework for Math Word Problems (2021, neutral): “Some works also leverage tree structures and graph information to improve performance (Wang et al., 2019b; Chiang and Chen, 2019; Liu et al., 2019a; Xie and Sun, 2019; Zhang et al., 2020).”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, methodology): “T-RNN (Wang et al., 2019) launches a two-stage system named as T-RNN that ﬁrst predicts a tree-structure template to be ﬁlled, and then accomplishes the template with operators predicted by the recursive neural network.”
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.”
Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem (2020, methodology): “To resolve the equation duplication issues, various equation normalization methods are proposed in (Wang et al., 2018a, 2019) to generate a unique expression tree with the cost of losing the understanding of problem-solving steps in equation expressions.”
A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving (2020, methodology): “Effect of external knowledge: Table 2 shows the Models Accuracy RecursiveNN (Wang et al., 2019) 68.7% GTS (Xie and Sun, 2019) 74.3 results of ablation experiments conducted to reduce the amount of external knowledge incorporated into the model.”
Teacher-Student Networks with Multiple Decoders for Solving Math Word Problem (2020, methodology): “The recent studies have attempted to improve the generation of solution expressions using sequence-to-tree (Seq2Tree) models [Wang et al. , 2018a; Chiang and Chen, 2019; Wang et al. , 2019; Liu et al. , 2019; Xie and Sun, 2019].”
Math Word Problem Solving with Explicit Numerical Values (2021, methodology): “RecursiveNN (Wang et al., 2019) uses a recursive neural network on the predicted tree structure templates Tree-Decoder (Liu et al., 2019) is a seq2tree model with a tree structured decoder.”
Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, methodology): “T-RNN (Wang et al., 2019) used a two-stage model to generate expressions.”
Solving Linear Algebra by Program Synthesis (2021, methodology): “Techniques have included sequence-tosequence and graph-to-tree Transformers which achieve around 80% on Math23k and MAWPS datasets (Koncel-Kedziorski et al., 2016; Li et al., 2019; Wang et al., 2019; Zhang et al., 2020; Li et al., 2020; Wu et al., 2020; Qin et al., 2020; Lan et al., 2021).”
Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems (2020, methodology): “Recently, deep learning has opened a new direction towards automatic MWPs solving (Wang et al., 2017; Huang et al., 2018; Wang et al., 2018b, 2019; Xie and Sun, 2019; Chiang and Chen, 2019).”
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.”
Solving Math Word Problems with Teacher Supervision (2021, background): “…solvers are recently designed to ‘translate’ math problems into a mathematical expression via Seq2Seq models [Wang et al. , 2017; Wang et al. , 2018; Wang et al. , 2019; Li et al. , 2019; Xie and Sun, 2019; Zhang et al. , 2020b], which have a typical encoder-decoder structure: the encoder learns…”
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”
Tree-structured Decoding for Solving Math Word Problems (2019, methodology): “Wang et al. (2019) proposed a two-step pipeline method that ﬁrst generates a template with unknown operators, and then uses a recursive neural network to combine tree structure information and predict the operators.”
Point to the Expression: Solving Algebraic Word Problems Using the Expression-Pointer Transformer Model (2020, methodology): “However, recent neural models have only utilized ‘Op (operator/operand)’ tokens (Wang et al., 2017; Amini et al., 2019; Chiang and Chen, 2019; Huang et al., 2018; Wang et al., 2019), resulting in two issues: (1) the expression fragmentation issue and (2) the operandcontext separation issue.”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, background): “Recently, there emerges various question-answering tasks that require human-like reasoning abilities (Qi et al. 2015; Tu et al. 2014; Zhang et al. 2019; Dua et al. 2019; Hong et al. 2019; Zhu et al. 2020; Zhang et al. 2020b; Li et al. 2020b; Yu et al. 2020).”