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...
Saved in:
Main Authors: | , , |
---|---|
Other Authors: | |
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 |