Graph-to-Tree Learning for Solving Math Word Problems

By Jipeng Zhang, Lei Wang, Roy Ka-Wei Lee, Yi Bin, Yan Wang, Jie Shao, Ee-Peng Lim. 2020

213 citations recorded by the source corpus.

While the recent tree-based neural models have demonstrated promising results in generating solution expression for the math word problem (MWP), most of these models do not capture the relationships and order information among the quantities well. This results in poor quantity representations and incorrect solution expressions. In this paper, we propose Graph2Tree, a novel deep learning architecture that combines the merits of the graph-based encoder and tree-based decoder to generate better solution expressions. Included in our Graph2Tree framework are two graphs, namely the Quantity Cell Graph and Quantity Comparison Graph, which are designed to address limitations of existing methods by effectively representing the relationships and order information among the quantities in MWPs. We conduct extensive experiments on two available datasets. Our experiment results show that Graph2Tree outperforms the state-of-the-art baselines on two benchmark datasets significantly. We also discuss case studies and empirically examine Graph2Tree’s effectiveness in translating the MWP text into solution expressions.

Subfields: Artificial Intelligence, 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, positive): “Furthermore, we implement and compare 17 MWP solving models, including Seq2Seq, Seq2tree, Graph2Tree, and commonly-used non-pretrained models and pretrained models, on 4 widely-used single equation generation benchmark datasets and 2 multiple equations generation benchmarks.”
Are NLP Models really able to Solve Simple Math Word Problems? (2021, methodology): “Following the setting of Zhang et al. (2020), the arithmetic word problems from MAWPS are divided into ﬁve folds, each of equal test size.”
Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, methodology): “What is the dividend? form of a tree structure, which is adopted in recent research efforts (Xie and Sun, 2019; Zhang et al., 2020; Patel et al., 2021; Wu et al., 2021).”
Generate & Rank: A Multi-task Framework for Math Word Problems (2021, neutral): “In addition, previous works (Liu et al., 2019a; Xie and Sun, 2019; Zhang et al., 2020) ﬁnd that the performance of generation models degrades fast as the expression gets longer.”
Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, background): “Graph2Tree considered the structure information of text descriptions, integrating the quantity cell graph and quantity comparison graph, so it achieves sub-optimal performance in all models.”
Solving Math Word Problems with Teacher Supervision (2021, methodology): “Graph2Tree [ Zhang et al. , 2020b ] trained by samples including Problem1 gives a wrong so-lution to Problem2.”
A Survey of Deep Learning for Mathematical Reasoning (2022, unknown): “The graph-based information can also be embedded when encoding the input mathematical sequences (Zhang et al., 2020b; Shen and Jin, 2020; Li et al., 2020b; Wu et al., 2021a).”
A Review on Large Language Models: Architectures, Applications, Taxonomies, Open Issues and Challenges (2024, methodology): “The GPT model aids the students in converting the math word problems into representative equations [143].”
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).”
MWP-BERT: A Strong Baseline for Math Word Problems (2021, methodology): “Graph2Tree (Zhang et al., 2020b) constructs two graphs during data pre-processing to extract extra relationships from text descriptions.”
DAGN: Discourse-Aware Graph Network for Logical Reasoning (2021, methodology): “Graph-based methods (Qiu et al., 2019; De Cao et al., 2019; Cao et al., 2019; Ran et al., 2019; Chen et al., 2020b; Xu et al., 2020b; Zhang et al., 2020) explicitly model the reasoning process with constructed graphs, then learn and update features through message passing based on graphs.”
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).”
HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem (2021, methodology): “With the advantages of automatic feature extraction and strong generality, deep learning methods especially seq2seq models have been widely used in recent studies (Wang, Liu, and Shi 2017; Huang et al. 2018; Wang et al. 2019; Xie and Sun 2019; Wang et al. 2018c; Zhang et al. 2020).”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, unknown): “…and Hajishirzi 2018) 51.9 CNN (Robaidek, Koncel-Kedziorski, and Hajishirzi 2018) 42.3 DNS (Wang, Liu, and Shi 2017) 58.1 Seq2seqET (Wang et al. 2018) 66.7 Stack-Decoder (Chiang and Chen 2019) 65.8 T-RNN (Wang et al. 2019) 66.9 GTS (Xie and Sun 2019) 74.3 Graph2Tree (Zhang et al. 2020a) 74”
Distilling Reasoning Capabilities into Smaller Language Models (2022, background): “Decomposing Multi-Step Reasoning Tasks Solving multi-step reasoning tasks like MWPs has been a popular area of research for the last couple of years (Kushman et al., 2014; Hosseini et al., 2014; Roy et al., 2015; Amini et al., 2019; Zhang et al., 2020; Shridhar et al., 2022; Opedal et al., 2023).”
A Weakly Supervised Model for Solving Math word Problems (2021, methodology): “Graph2Tree (Zhang et al., 2020) consists of a graph-based encoder which captures the relationships and order information among the quantities and a tree-based decoder that generates expression tree in a goal-driven manner.”
Math Word Problem Solving with Explicit Numerical Values (2021, background): “Zhang et al. (2020b) connects each number in the problem with nearby nouns to enrich the problem representations.”
A Bottom-Up DAG Structure Extraction Model for Math Word Problems (2021, methodology): “Then Zhang et al. (2020) extended this model from Seq2Tree to Graph2Tree by adding a graph encoder.”
Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems (2021, unknown): “Graph2Tree 4 (Zhang et al., 2020) design a graph-based encoder for representing the relationships and order information among the quantities.”