Abstract
Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; 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 neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment.
Highlights
Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated
Numerosity turned out to be the primary driver of both humans’ and deep networks’ responses in a numerosity comparison task, even when non-numerical visual cues were included as predictors of behavioral choices
Numerosity was a critical factor in shaping the internal representations emerging from unsupervised deep learning, showing that number was spontaneously encoded in the model even when no number-related decision had to be carried out
Summary
Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. It has been repeatedly pointed out that numerosity judgments can be modulated by non-numerical perceptual cues that usually co-vary with number, such as cumulative surface area[18], total item perimeter[19] and convex hull[20], over which it is impossible to exert full experimental control and which can hinder numerosity discrimination when carrying incongruent information[21,22] These findings have led to the proposal that numerosity is indirectly estimated from non-numerical visual features, thereby calling into question the existence of a dedicated system for numerosity perception[23]. We used representational similarity analysis[42] to investigate the encoding of numerosity and continuous visual features in the deep networks’ internal representations, thereby shedding light on whether spontaneous sensitivity to number emerges (from unsupervised learning) in the absence of any explicit task
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