Learning from Natural Images Untangles Number Sense

Numerical cognition is a simple yet fundamental ability that remains challenging for modern vision-language models. Number sense is already present in numerically naïve animals, suggesting that it can emerge without explicit numerical learning. Deep neural networks provide a related observation, with numerosity-selective units appearing after training on unrelated natural-image tasks and even before any training. However, these findings leave unresolved whether visual learning contributes beyond the spontaneous emergence of numerical selectivity. Human development provides a clue, as children become better at making judgments in which numerosity and proportion conflict. Here, we introduce a geometric framework to trace how representations of these two quantities change across learning. Although both untrained and pretrained networks exhibited unit-level numerosity selectivity and similar basic comparison performance, their population-level organization differed substantially. Numerosity and proportion representations overlapped strongly before training but became separated after natural-image learning, supporting more robust readout under conflict. Importantly, this reorganization did not require supervised category learning, as self-supervised learning produced comparable separation while shuffled-label training did not. Together, our results suggest that rudimentary number sense may emerge spontaneously, while structured visual learning reorganizes latent quantity information into representations that enable more independent and robust decoding.