Wefind that humans are indeed sensitivetoEuclidean geometry and generalize strongly from a few visual examples of a geometric concept.

Participants were recruited on Prolific [Palan and Schitter, 2018], and compensated withanhourlywageof $15.8. SeeFigure 1foranexample of a survey question given to participants,hostedonQualtrics. You may decline to answer any or all of the following questions. Your anonymity is assured; the researchers who have requested your participation will not receive any personalinformationaboutyou". A.4 FeatureVisualizations We provide visualizations of low-level features from ResNet50 and the Vision Transformer on a variety of rendered Geoclidean images. In contrast, the third Geoclideantask is difficult for both vision models, highlighting the intended difficulty of Euclidean geometric reasoning -why our task is especially interesting.

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.

Euclidean geometry is among the earliest forms of mathematical thinking.

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.