Learning Fine-Grained Expressions to Solve Math Word Problems

By Danqing Huang, Shuming Shi, Chin-Yew Lin, Jian Yin. 2017

91 citations recorded by the source corpus.

This paper presents a novel template-based method to solve math word problems. This method learns the mappings between math concept phrases in math word problems and their math expressions from training data. For each equation template, we automatically construct a rich template sketch by aggregating information from various problems with the same template. Our approach is implemented in a two-stage system. It first retrieves a few relevant equation system templates and aligns numbers in math word problems to those templates for candidate equation generation. It then does a fine-grained inference to obtain the final answer. Experiment results show that our method achieves an accuracy of 28.4% on the linear Dolphin18K benchmark, which is 10% (54% relative) higher than previous state-of-the-art systems while achieving an accuracy increase of 12% (59% relative) on the TS6 benchmark subset.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Natural Language Processing

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Citations in the corpus

Are NLP Models really able to Solve Simple Math Word Problems? (2021, background): “com/arkilpatel/SVAMP 2018), semantic parsing (Huang et al., 2017) and most recently deep learning (Wang et al.”
A Goal-Driven Tree-Structured Neural Model for Math Word Problems (2019, methodology): “…1985; Bakman, 2007; Yuhui et al. , 2010], statistical machine learning methods [Kushman et al. , 2014; Zhou et al. , 2015; Mitra and Baral, 2016; Roy and Roth, 2018] and semantic parsing methods [ Shi et al. , 2015; Koncel-Kedziorski et al. , 2015; Huang et al. , 2017] RNN [Wang et al. , 2017].”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, background): “An initial study in this area can be found in (Wang et al. 2017; Huang et al. 2017).”
EQUATE: A Benchmark Evaluation Framework for Quantitative Reasoning in Natural Language Inference (2019, background): “tic word problems (Hosseini et al., 2014; Mitra and Baral, 2016; Zhou et al., 2015; Upadhyay et al., 2016; Huang et al., 2017; Kushman et al., 2014a; Koncel-Kedziorski et al., 2015; roy; Roy, 2017; Ling et al., 2017a).”
Mapping to Declarative Knowledge for Word Problem Solving (2017, background): “Kushman et al. (2014) introduces a template based approach to handle general algebra word problems and several works have later proposed improvements over this approach (Zhou et al., 2015; Upadhyay et al., 2016; Huang et al., 2017).”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, methodology): “, 2016) and semantic parsing-based methods (Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017), these methods do not need hand-crafted features and achieve high performance on large datasets.”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, methodology): “In (Wang, Liu, and Shi 2017), the retrieval model is used if the similarity between a candidate and the query problem is larger than the threshold; otherwise, DNS is used.”
Graph-to-Tree Learning for Solving Math Word Problems (2020, methodology): “…divided into statistical machine learning based (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Zou and Lu, 2019a) and semantic parsing based (Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017; Zou and Lu, 2019b).”
A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving (2020, background): “Huang et al. (2017) formulated ﬁne-grained templates and aligned numbers in math word problems to those candidate templates.”
Tree-structured Decoding for Solving Math Word Problems (2019, background): “, 2015; Roy and Roth, 2015; Huang et al., 2017; Roy and Roth, 2018). Shi et al. (2015) defined a Dolphin language to connect math word problems and logical forms.”
HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem (2021, background): “Answer 22 Expression 2× (4+3+4) to evaluate problem representations in online education systems, where great progress has been achieved (Huang et al. 2017b; Yin et al. 2018, 2019).”
Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, background): “…2016; Mitra and Baral, 2016; Huang et al., 2016; Roy and Roth, 2018), semantic parsing methods (Shi et al., 2015; Koncelkedziorski et al., 2015; Huang et al., 2017; Liang et al., 2018a), to deep learning meth-ods (Ling et al., 2017; Wang et al., 2017, 2018b; Huang et al., 2018; Wang et al.,…”
Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning (2022, unknown): “To solve MWPs, one popular line of previous methods is to generate the intermediate expressions and execute them to get the ﬁnal answers (Huang et al., 2017; Roy & Roth, 2017; Amini et al., 2019).”
Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems (2020, methodology): “…al., 2015; Mitra and Baral, 2016; Huang et al., 2016; Roy and Roth, 2018),semantic parsing methods (Shi et al., 2015; Koncelkedziorski et al., 2015; Huang et al., 2017), and deep learning methods (Ling et al., 2017; Wang et al., 2017, 2018b; Huang et al., 2018; Wang et al., 2018a; Xie and Sun,…”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, methodology): “…Chen 2015; Mitra and Baral 2016; Roy and Roth 2017; Huang et al. 2016), semantic-parsing meth-ods (Shi et al. 2015; Koncel-Kedziorski et al. 2015; Huang et al. 2017) to recent deep learning methods (Ling et al. 2017; Wang, Liu, and Shi 2017; Huang et al. 2018; Robaidek, Koncel-Kedziorski, and…”
Point to the Expression: Solving Algebraic Word Problems Using the Expression-Pointer Transformer Model (2020, methodology): “The CASS-hybrid is the best-performing hybrid model of the CASSRL and Huang et al. (2017)’s model using hand-crafted features.”
Using Intermediate Representations to Solve Math Word Problems (2018, methodology): “To explore the generalization ability of the neural approach and better guide our future work, we compare the problems solved by our neural-based model with the rule-based model (Shi et al., 2015) and the feature-based model (Huang et al., 2017).”
Translating a Math Word Problem to an Expression Tree (2018, methodology): “…Mitra and Baral, 2016; Roy and Roth, 2018) and semantic parsing-based methods (Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017) are proposed to tackle this problem, yet they still require considerable manual ∗ The work was done when Lei Wang and Deng Cai…”
Investigating Math Word Problems using Pretrained Multilingual Language Models (2021, background): “Various approaches have been proposed to solve MWPs. Template-based approaches (Kushman et al., 2014; Zhou et al., 2015; Upadhyay et al., 2016; Huang et al., 2017) are widely adopted as numbers appeared in the expressions are usually sparse in the representation space and the expressions may fall…”