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...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/171217 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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