A dynamical recurrent neural network model for visual perception of numerosity

Abstract

Humans have an inherent ability to visually perceive small numerosities (the cardinality of a set). According to several studies, the LIP and other IPS regions of the brain include the neurological substrates for the processes related to numbers. Computational models play a crucial role in investigating the computations and dynamics behind the perception of numbers. Existing models of number perception simulate a few of the fundamental aspects of number perception, such as size and distance effects. However, most models usually work for a limited range of numbers and lack explanations for important behavioral characteristics like adaptation effects. In this study, we use a network of neurons with self-excitatory and mutual inhibitory properties to build a computational model of number perception. We assume that the network's mean activation at steady-state can encode numerosity when it increases monotonically with Setsize (the input to the network). By optimizing the total number of inhibition strengths required so that the combined monotonic regions cover the full stretch of numbers, we get three ranges of numbers (1:4, 5:17, and 21:50). This division of numbers into three parts closely matches the elbows in numerosity perception discovered in behavioral studies. Later in the study, we devised a method to decode the mean activation into a continuous scale of numbers ranging from 1 to 50. Furthermore, we suggest a mechanism for selecting inhibition strength based on current inputs, allowing the network to work for the entire range of numerosities. Our model provides novel perspectives on how our brain can generate various behavioral phenomena, such as the influences of continuous visual attributes and adaptation effects on perceived numerosity.