A visual sense of number emerges from the dynamics of a recurrent on-center off-surround neural network

• Subitization and estimation emerge from the dynamics of a single recurrent network.
• Unified account of various classical numerical cognition effects.
• Novel formulation of energy function enables comprehensive parametric investigation.
• Reaction time (RT) estimate for enumeration experiments from simulation.
• Novel testable prediction about a possible asymmetric switch cost in enumeration.

It has been proposed that the ability of humans to quickly perceive numerosity involves a visual sense of number. Different paradigms of enumeration and numerosity comparison have produced a gamut of behavioral and neuroimaging data, but there has been no unified conceptual framework that can explain results across the entire range of numerosity. The current work tries to address the ongoing debate concerning whether the same mechanism operates for enumeration of small and large numbers, through a computational approach. We describe the workings of a single-layered, fully connected network characterized by self-excitation and recurrent inhibition that operates at both subitizing and estimation ranges. We show that such a network can account for classic numerical cognition effects (the distance effect, Fechner׳s law, Weber fraction for numerosity comparison) through the network steady state activation response across different recurrent inhibition values. The model also accounts for fMRI data previously reported for different enumeration related tasks. The model also allows us to generate an estimate of the pattern of reaction times in enumeration tasks. Overall, these findings suggest that a single network architecture can account for both small and large number processing.