Learning from Explicit and Implicit Supervision Jointly For Algebra Word Problems

By Shyam Upadhyay, Ming-Wei Chang, Kai-Wei Chang, Wen-tau Yih. 2016

52 citations recorded by the source corpus.

Automatically solving algebra word problems has raised considerable interest recently. Existing state-of-the-art approaches mainly rely on learning from human annotated equations. In this paper, we demonstrate that it is possible to efﬁciently mine algebra problems and their numerical solutions with little to no manual effort. To leverage the mined dataset, we propose a novel structured-output learning al-gorithm that aims to learn from both explicit (e.g., equations) and implicit (e.g., solutions) supervision signals jointly . Enabled by this new algorithm, our model gains 4.6% absolute improvement in accuracy on the A LG - 514 benchmark compared to the one without using implicit supervision. The ﬁnal model also outperforms the current state-of-the-art approach by 3%.

Subfields: Artificial Intelligence, Natural Language Processing

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Citations in the corpus

Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, background): “…the problems (Kushman et al., 2014; Hosseini et al., 2014; Roy et al., 2015; Roy and Roth, 2015; Koncel-Kedziorski et al., 2015; Roy et al., 2016; Upadhyay et al., 2016; Upadhyay and Chang, 2017; Roy and Roth, 2018; Wang et al., 2018 In terms of how to learn the model for solving math word…”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, background): “proposed a structured-output learning framework to learn both explicit and implicit signals jointly (Upadhyay et al. 2016).”
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).”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, background): “Upadhyay et al. proposed a structured-output learning framework to learn both explicit and implicit signals jointly (Upadhyay et al. 2016).”
A Weakly Supervised Model for Solving Math word Problems (2021, methodology): “Upadhyay et al. (2016) employ a semi-supervised approach by learning to predict templates and corresponding alignments using both explicit and implicit super-vision.”
NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks (2022, background): “Difﬁculty of questions were increased in subsequent datasets (Roy and Roth, 2016), (Upadhyay et al., 2016).”
A Meaning-Based Statistical English Math Word Problem Solver (2018, methodology): “, 2014), which make all related decisions based on a set of rules; (2) Purely statistics-based approaches (Kushman et al., 2014; Roy et al., 2015; Zhou et al., 2015; Upadhyay et al., 2016), in which all related decisions are done via a statistical classifier; (3) DNNbased approaches (Ling et al.”
Maximum Margin Reward Networks for Learning from Explicit and Implicit Supervision (2017, background): “Upadhyay et al. (2016) ﬁrst proposed the idea of learning from implicit supervision, and is the most related paper to our work.”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, background): “Upadhyay et al. (2016), Zhou, Dai, and Chen (2015), and Kushman et al. (2014) use mixed supervision, where one dataset has only annotated equations, and the other has only ﬁnal answers.”
Learning Fine-Grained Expressions to Solve Math Word Problems (2017, methodology): “Upadhyay et al. (2016) follows their approach and leverage math word problems without equation annotation as external resources.”
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…”
Using Intermediate Representations to Solve Math Word Problems (2018, background): “Feature-based approaches contain two stages: (1) generate equation candidates; They either replace numbers of existing equations in the training data as new equations (Kushman et al., 2014; Zhou et al., 2015; Upadhyay et al., 2016), or enumerate possible combinations of math operators and numbers an”
The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers (2018, background): “To resolve the issue, in [45], Upadhyay et al. attempted to exploit the large number of algebra word problems that have been posted and discussed in online forums.”
Point to the Expression: Solving Algebraic Word Problems Using the Expression-Pointer Transformer Model (2020, methodology): “Upadhyay et al. (2016) designed a model using a set of hand-crafted features similar to those used by Zhou et al. (2015).”
LILA: A Unified Benchmark for Mathematical Reasoning (2022, methodology): “…datasets testing addition-subtraction (Hosseini et al., 2014), templated questions with equations as parameters (Kushman et al., 2014) and other forms of arithmetic reasoning (Koncel-Kedziorski et al., 2015; Roy and Roth, 2016; Upadhyay et al., 2016; Roy and Roth, 2017, 2018; Ling et al., 2017).”
Neural Math Word Problem Solver with Reinforcement Learning (2018, background): “Kushman et al. (2014), Zhou et al. (2015), Upadhyay et al. (2016) use features such as dependency path between two numbers.”