Learning to Solve Geometry Problems from Natural Language Demonstrations in Textbooks

By Mrinmaya Sachan, Eric P. Xing. 2017

55 citations recorded by the source corpus.

Humans as well as animals are good at imitation. Inspired by this, the learning by demonstration view of machine learning learns to perform a task from detailed example demonstrations. In this paper, we introduce the task of question answering using natural language demonstrations where the question answering system is provided with detailed demonstrative solutions to questions in natural language. As a case study, we explore the task of learning to solve geometry problems using demonstrative solutions available in textbooks. We collect a new dataset of demonstrative geometry solutions from textbooks and explore approaches that learn to interpret these demonstrations as well as to use these interpretations to solve geometry problems. Our approaches show improvements over the best previously published system for solving geometry problems.

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): “Recently, researchers have started focusing on solving such MWPs, e.g. multiple-unknown linear word problems (Huang et al., 2016a), geometry (Sachan and Xing, 2017) and probability (Amini et al., 2019), believing that existing work can handle one-unknown arithmetic MWPs well (Qin et al., 2020).”
Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering (2022, background): “An example of learning from explanations in the scientific domain is proposed in [51] where the model interprets demonstrative solutions to solve geometry problems.”
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).”
GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning (2021, background): “, 2015b) or not release their codes (Sachan and Xing, 2017; Sachan, 2020).”
A Survey of Deep Learning for Mathematical Reasoning (2022, unknown): “Some early datasets are proposed to facilitate research in this domain (Seo et al., 2015; Alvin et al., 2017; Sachan et al., 2017; Sachan and Xing, 2017).”
Large Language Models for Mathematical Reasoning: Progresses and Challenges (2024, unknown): “An example can be seen as follows and Table 3 (Seo et al., 2015) 186 G EO S++ (Sachan et al., 2017) 1.4K G EO S-OS (Sachan and Xing, 2017) 2.2K G EOMETRY 3K (Lu et al., 2021) 3K G EO QA (Chen et al., 2021a) 5K U NI G EO (Chen et al., 2022) 14.5K”
Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning (2021, background): “…appropriate data, most early works on automated geometry systems focus on geometry theorem proving (Wen-Tsun, 1986; Chou et al., 1996; Yu et al., 2019; Gan et al., 2019), problem synthesis (Alvin et al., 2014), diagram parsing (Seo et al., 2014), as well as problem formalization (Gan and Yu, 2018).”