Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems

By Ting-Rui Chiang, Yun-Nung (Vivian) Chen. 2018

127 citations recorded by the source corpus.

Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the problem texts, this paper presents a neural approach to automatically solve math word problems by operating symbols according to their semantic meanings in texts. This paper views the process of generating equation as a bridge between the semantic world and the symbolic world, where the proposed neural math solver is based on an encoder-decoder framework. In the proposed model, the encoder is designed to understand the semantics of problems, and the decoder focuses on tracking semantic meanings of the generated symbols and then deciding which symbol to generate next. The preliminary experiments are conducted in a dataset Math23K, and our model significantly outperforms both the state-of-the-art single model and the best non-retrieval-based model over about 10% accuracy, demonstrating the effectiveness of bridging the symbolic and semantic worlds from math word problems.

Subfields: Artificial Intelligence, Natural Language Processing

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Citations in the corpus

Chain of Thought Prompting Elicits Reasoning in Large Language Models (2022, background): “Their work is a remarkable contrast to the literature using formal languages to reason (Roy et al., 2015; Chiang and Chen, 2019; Amini et al., 2019; Chen et al., 2019).”
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): “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): “Wang et al. (2017) proposed the Math23k dataset and presented a sequence-to-sequence (seq2seq) approach to generate the mathematical expression (Chiang and Chen, 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).”
Continual Pre-training of Language Models for Math Problem Understanding with Syntax-Aware Memory Network (2022, methodology): “Numerous deep learning based methods have been proposed to tackle the MWP task, including Seq2Seq (Chiang and Chen, 2019; Li et al., 2019), Seq2Tree (Wang et al., 2019; Qin et al., 2020), and Pre-trained Language Models (Kim et al., 2020; Liang et al., 2021).”
Graph-to-Tree Learning for Solving Math Word Problems (2020, background): “S-Aligned (Chiang and Chen, 2019) designs the decoder with a stack to track the semantic meanings of operands.”
The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers (2018, methodology): “This is an emerging research direction for MWP solvers and we observed multiple instances, including Deep Neural Solver [14], Seq2SeqET [15], StackDecoder [16], MathDQN [17], CASS [18], T-RNN [19].”
Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems (2020, methodology): “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…”
Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems (2020, methodology): “For decoding, inspired by previous works (Xie and Sun, 2019; Chiang and Chen, 2019), we build a semantically-aligned tree decoder to decide which”
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.”
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).”
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.”
Tree-structured Decoding for Solving Math Word Problems (2019, methodology): “Chiang and Chen (2018) used the copy mechanism to improve the semantic representation of quantities.”
Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, methodology): “S-Aligned (Chiang and Chen, 2019) adopted a stack to track the semantic meanings of numbers.”
A Survey of Deep Learning for Mathematical Reasoning (2022, unknown): “For instance, deep learning-based math word problem solvers have adopted a sequence-to-sequence framework with attention mechanisms to generate mathematical expressions as intermediate steps (Wang et al., 2018a; Chiang and Chen, 2019).”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, background): “2017) to recent deep learning methods (Ling et al. 2017; Wang, Liu, and Shi 2017; Huang et al. 2018; Robaidek, Koncel-Kedziorski, and Hajishirzi 2018; Wang et al. 2018, 2019; Chiang and Chen 2019; Xie and Sun 2019; Zhang et al. 2020a).”
Teaching Algorithmic Reasoning via In-context Learning (2022, methodology): “Mathematical reasoning (Chiang and Chen, 2018; Saxton et al., 2019) has been subject of interest for a long time.”
Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, methodology): “Again, following prior works (Wang et al., 2017; Chiang and Chen, 2019; Xie and Sun, 2019), we use answer accuracy as the evaluation metric: if the calculated value of the predicted equation tree equals to the true answer, it is thought as correct since the predicted expression”