EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry
Abstract
In this paper, we present a deep learningbased framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedgeandcompass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask RCNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a stepbystep construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2301.13007
 arXiv:
 arXiv:2301.13007
 Bibcode:
 2023arXiv230113007W
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Artificial Intelligence;
 Computer Science  Machine Learning
 EPrint:
 Accepted by 2nd MATHAI Workshop at NeurIPS'22