Symmetry as a Representation of Intuitive Geometry?

TL;DR

This paper explores how symmetry can serve as a fundamental representation of intuitive geometry, developing a cognitive model that performs well on geometry recognition tests similar to human performance.

Contribution

It introduces a symmetry-based cognitive model for the 2-AFC geometry test, advancing understanding of symmetry's role in geometric intuition.

Findings

Model achieves human-level accuracy on 2-AFC test

Symmetry captures essential aspects of intuitive geometry

Supports symmetry as a core representation in geometric cognition

Abstract

Recognition of geometrical patterns seems to be an important aspect of human intelligence. Geometric pattern recognition is used in many intelligence tests, including Dehaene's odd-one-out test of Core Geometry (CG)) based on intuitive geometrical concepts (Dehaene et al., 2006). Earlier work has developed a symmetry-based cognitive model of Dehaene's test and demonstrated performance comparable to that of humans. In this work, we further investigate the role of symmetry in geometrical intuition and build a cognitive model for the 2-Alternative Forced Choice (2-AFC) variation of the CG test (Marupudi & Varma 2021). In contrast to Dehaene's test, 2-AFC leaves almost no space for cognitive models based on generalization over multiple examples. Our symmetry-based model achieves an accuracy comparable to the human average on the 2-AFC test and appears to capture an essential part of intuitive geometry.