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

2025-11-19

AI Summary

Whether visual model training spontaneously recapitulates the cognitive developmental trajectory of geometric and numerical concepts observed in human children remains unknown. Method: We trained a ResNet-50 on standard image classification without explicit mathematical supervision and systematically analyzed the dynamic evolution of its internal feature representations. Representational development was quantitatively assessed using cognitive science paradigms—including mental number line alignment, Euclidean vs. topological judgments, and shape invariance—mirroring behavioral assays used in developmental psychology. Contribution/Results: We report the first evidence that geometric sensitivity (e.g., shape invariance) emerges early in training, while a numerically ordered, human-like “mental number line” representation gradually crystallizes later. Crucially, the model’s representational stages align significantly with established human developmental milestones (p < 0.01). These findings demonstrate that purely visual experience suffices to drive the self-organized emergence of abstract mathematical cognition, offering a novel paradigm bridging AI cognitive modeling and developmental neuroscience.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Representation Learning for Vision
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Investigates developmental alignment between computer vision models and human mathematical concept progression
• Examines whether CV training improvements mirror children's geometric and numerical development trajectories
• Assesses cognitive alignment in geometry, topology and mental number line representations

Innovation

• Computer vision models simulate human geometric concept development
• ResNet-50 training mirrors children's numerical representation progression
• Models show developmental alignment for topology and number concepts