Spiking neural networks evolved to perform multiplicative operations

Abstract

Multiplicative or divisive changes in tuning curves of individual neurons to one stimulus (“input”) as another stimulus (“modulation”) is applied, called gain modulation, play an important role in perception and decision making. Since the presence of modulatory synaptic stimulation results in a multiplicative operation by proportionally changing the neuronal input-output relationship, such a change affects the sensitivity of the neuron but not its selectivity. Multiplicative gain modulation has commonly been studied at the level of single neurons. Much less is known about arithmetic operations at the network level. In this work we have evolved small networks of spiking neurons in which the output neurons respond to input with non-linear tuning curves that exhibit gain modulation—the best network showed an over 3-fold multiplicative response to modulation. Interestingly, we have also obtained a network with only 2 interneurons showing an over 2-fold response.