Computer Vision Modeling of the Development of Geometric and Numerical Concepts in Humans

TL;DR

This study investigates whether computer vision models develop geometric and numerical concepts in a manner similar to human developmental progress, revealing partial alignment and potential for understanding human mathematical development.

Contribution

It demonstrates that CV models exhibit developmental alignment with human learning trajectories for some geometric and numerical concepts, advancing understanding of AI-human cognitive parallels.

Findings

Developmental alignment observed for Euclidean Geometry and Number line concepts.

Partial alignment for geometric classes like Topology but not for others.

CV models show promise for modeling human mathematical development.

Abstract

Mathematical thinking is a fundamental aspect of human cognition. Cognitive scientists have investigated the mechanisms that underlie our ability to thinking geometrically and numerically, to take two prominent examples, and developmental scientists have documented the trajectories of these abilities over the lifespan. Prior research has shown that computer vision (CV) models trained on the unrelated task of image classification nevertheless learn latent representations of geometric and numerical concepts similar to those of adults. Building on this demonstrated cognitive alignment, the current study investigates whether CV models also show developmental alignment: whether their performance improvements across training to match the developmental progressions observed in children. In a detailed case study of the ResNet-50 model, we show that this is the case. For the case of geometry and topology, we find developmental alignment for some classes of concepts (Euclidean Geometry, Geometrical Figures, Metric Properties, Topology) but not others (Chiral Figures, Geometric Transformations, Symmetrical Figures). For the case of number, we find developmental alignment in the emergence of a human-like ``mental number line'' representation with experience. These findings show the promise of computer vision models for understanding the development of mathematical understanding in humans. They point the way to future research exploring additional model architectures and building larger benchmarks.