Geoclidean: Few-Shot Generalization in Euclidean Geometry
- URL: http://arxiv.org/abs/2211.16663v1
- Date: Wed, 30 Nov 2022 01:17:22 GMT
- Title: Geoclidean: Few-Shot Generalization in Euclidean Geometry
- Authors: Joy Hsu, Jiajun Wu, Noah D. Goodman
- Abstract summary: Euclidean geometry is among the earliest forms of mathematical thinking.
Will computer vision models trained on natural images show the same sensitivity to Euclidean geometry?
We introduce Geoclidean, a domain-specific language for Euclidean geometry.
- Score: 36.203651858533
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Euclidean geometry is among the earliest forms of mathematical thinking.
While the geometric primitives underlying its constructions, such as perfect
lines and circles, do not often occur in the natural world, humans rarely
struggle to perceive and reason with them. Will computer vision models trained
on natural images show the same sensitivity to Euclidean geometry? Here we
explore these questions by studying few-shot generalization in the universe of
Euclidean geometry constructions. We introduce Geoclidean, a domain-specific
language for Euclidean geometry, and use it to generate two datasets of
geometric concept learning tasks for benchmarking generalization judgements of
humans and machines. We find that humans are indeed sensitive to Euclidean
geometry and generalize strongly from a few visual examples of a geometric
concept. In contrast, low-level and high-level visual features from standard
computer vision models pretrained on natural images do not support correct
generalization. Thus Geoclidean represents a novel few-shot generalization
benchmark for geometric concept learning, where the performance of humans and
of AI models diverge. The Geoclidean framework and dataset are publicly
available for download.
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