Numerosity Sense in Artificial Neural Networks

Abstract

The ability to approximately assess the number of objects in the set is observed in humans as well as animals. The mechanism of emergence of this ability is still an open research question. In this work, we consider approaching this question with the help of artificial neural networks from two perspectives: as an emergent property of interaction with the objects in the world through actions (as proposed by [KP20]), and as an emergent property of bottom-up projections of visual system (as proposed by [KJB+21]). The first approach leads to topological organization of the embedding space of the network in a linear monotonic way with respect to cardinality of embedded samples that resembles "mental number line". The second approach leads to the detection of numerosity-sensitive artificial units with tuning properties that resemble tuning properties of real neurons recorded in monkey prefrontal cortex. Through a series of control experiments we demonstrate that representation that emerges in artificial units of both models does not disentangle abstract property of numerosity of a set from visual properties of objects constituting this set that are confounded with numerosity.