World Models for Math Story Problems

Andreas Opedal, Niklas Stoehr, Abulhair Saparov, Mrinmaya Sachan


Abstract
Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.
Anthology ID:
2023.findings-acl.579
Volume:
Findings of the Association for Computational Linguistics: ACL 2023
Month:
July
Year:
2023
Address:
Toronto, Canada
Editors:
Anna Rogers, Jordan Boyd-Graber, Naoaki Okazaki
Venue:
Findings
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
9088–9115
Language:
URL:
https://aclanthology.org/2023.findings-acl.579
DOI:
10.18653/v1/2023.findings-acl.579
Bibkey:
Cite (ACL):
Andreas Opedal, Niklas Stoehr, Abulhair Saparov, and Mrinmaya Sachan. 2023. World Models for Math Story Problems. In Findings of the Association for Computational Linguistics: ACL 2023, pages 9088–9115, Toronto, Canada. Association for Computational Linguistics.
Cite (Informal):
World Models for Math Story Problems (Opedal et al., Findings 2023)
Copy Citation:
PDF:
https://aclanthology.org/2023.findings-acl.579.pdf
Video:
 https://aclanthology.org/2023.findings-acl.579.mp4