CNN models' sensitivity to numerosity concepts

Published: 28 Oct 2023, Last Modified: 16 Nov 2023MATH-AI 23 PosterEveryoneRevisionsBibTeX
Keywords: cognitive science, computer vision, CNN, cognitive modeling, number line, numerosity
TL;DR: CNN models show human-like magnitude representations of number and a latent mental number line representation.
Abstract: The nature of number is a classic question in the philosophy of mathematics. Cognitive scientists have shown that numbers are mentally represented as magnitudes organized as a mental number line (MNL). Here we ask whether CNN models, in learning to classify images, also learn about number and numerosity ‘for free’. This was the case. A representative model showed the distance, size, and ratio effects that are the signatures of magnitude representations in humans. An MDS analysis of their latent representations found a close resemblance to the MNL documented in people. These findings challenge the developmental science proposal that numbers are part of the ‘core knowledge’ that all human infants possess, and instead serve as an existence proof of the learnability of numerical concepts.
Submission Number: 37