EuclidNet: deep visual reasoning for constructible problems in geometry

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 constr...

Full description

Saved in:
Bibliographic Details
Main Authors: Wong, Man Fai, Qi, Xintong, Tan, Chee Wei
Other Authors: School of Computer Science and Engineering
Format: Article
Language:English
Published: 2023
Subjects:
Online Access:https://hdl.handle.net/10356/171217
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-171217
record_format dspace
spelling sg-ntu-dr.10356-1712172023-10-20T15:35:48Z EuclidNet: deep visual reasoning for constructible problems in geometry Wong, Man Fai Qi, Xintong Tan, Chee Wei School of Computer Science and Engineering Engineering::Computer science and engineering Geometric Reasoning Geometry Construction 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. Ministry of Education (MOE) Published version This research was supported in part by the Ministry of Education, Singapore, under its Academic Research Fund (No. 022307). 2023-10-17T06:06:46Z 2023-10-17T06:06:46Z 2022 Journal Article Wong, M. F., Qi, X. & Tan, C. W. (2022). EuclidNet: deep visual reasoning for constructible problems in geometry. Adv. Artif. Intell. Mach. Learn.(2023), 3(1):839-852, 3(1), 839-852. https://dx.doi.org/10.54364/aaiml.2023.1152 2582-9793 https://hdl.handle.net/10356/171217 10.54364/aaiml.2023.1152 1 3 839 852 en 022307 Adv. Artif. Intell. Mach. Learn.(2023), 3(1):839-852 © 2023 Man Fai Wong, et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Computer science and engineering
Geometric Reasoning
Geometry Construction
spellingShingle Engineering::Computer science and engineering
Geometric Reasoning
Geometry Construction
Wong, Man Fai
Qi, Xintong
Tan, Chee Wei
EuclidNet: deep visual reasoning for constructible problems in geometry
description 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.
author2 School of Computer Science and Engineering
author_facet School of Computer Science and Engineering
Wong, Man Fai
Qi, Xintong
Tan, Chee Wei
format Article
author Wong, Man Fai
Qi, Xintong
Tan, Chee Wei
author_sort Wong, Man Fai
title EuclidNet: deep visual reasoning for constructible problems in geometry
title_short EuclidNet: deep visual reasoning for constructible problems in geometry
title_full EuclidNet: deep visual reasoning for constructible problems in geometry
title_fullStr EuclidNet: deep visual reasoning for constructible problems in geometry
title_full_unstemmed EuclidNet: deep visual reasoning for constructible problems in geometry
title_sort euclidnet: deep visual reasoning for constructible problems in geometry
publishDate 2023
url https://hdl.handle.net/10356/171217
_version_ 1781793707397218304