EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry

TL;DR

EuclidNet is a deep learning framework that uses visual reasoning and recursive backtracking to solve complex geometric construction problems, aiding automated theorem proving.

Contribution

It introduces a neural network-based approach combining Mask R-CNN with recursive backtracking for solving constructible geometry problems.

Findings

Successfully applied to Japanese Sangaku geometry problems

Demonstrates capacity for deep visual reasoning in complex cases

Provides step-by-step construction guides for solutions

Abstract

In this paper, we present a deep learning-based 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 straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN 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 step-by-step 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.