A Neural Model of Multidigit Numerical Representation and Comparison

The Extended Spatial Number Network (ESpaN) is a neural model that simulates processing of high-level numerical stimuli such as multi-digit numbers. The ESpaN model targets the explanation of human psychophysical data, such as error rates and reaction times, about multi-digit (base 10) numerical stimuli, and describes how such a competence can develop through learning. The model suggests how the brain represents and processes an open-ended set of numbers and their regularities, such as the place-value structure, with finite resources in the brain. The model does that by showing how a multi-digit spatial number map forms through interactions with learned semantic categories that symbolize separate digits, as well as place markers like "tens," "hundreds," "thousands," etc. When number-stimuli are presented to the network, they trigger learning of associations between specific semantic categories and corresponding spatial locations of the spatial number map that together build a multi-digit spatial representation. Training of the network is aimed at portraying the process of development of human numerical competence during the first years of a child's life. The earlier SpaN model proposed a spatial number map, which both human and animal possess in their Where cortical processing stream, that can explain many data about analog numerical representation and comparison. The ESpaN model shows how learned cognitive categories in the What cortical processing stream can extend numerical competence to multi-digit numbers with a place-value structure. The ESpaN model hereby suggests how cortical cognitive and spatial processes can utilize a learned What-and-Where interstream interaction to control the development of multidigit numerical abilities.