Perception of visual numerosity in humans and machines

Abstract: Numerosity perception is foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representation; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep networks on the same numerosity comparison task that was administered to humans, using a stimulus space that allows to measure the contribution of non-numerical features. Our model accurately simulated the psychophysics of numerosity perception and the associated developmental changes: discrimination was driven by numerosity information, but non-numerical features had a significant impact, especially early during development. Representational similarity analysis further highlighted that both numerosity and continuous magnitudes were spontaneously encoded even when no task had to be carried out, demonstrating that numerosity is a major, salient property of our visual environment.