A Simple Neural Network Exhibiting Selective Activation of Neuronal Ensembles: From Winner-Take-All to Winners-Share-All

Abstract

A neuroecological equation of the Lotka-Volterra type for mean firing rate is derived from the conventional membrane dynamics of a neural network with lateral inhibition and self-inhibition. Neural selection mechanisms employed by the competitive neural network receiving external inputs are studied with analytic and numerical calculations. A remarkable findings is that the strength of lateral inhibition relative to that of self-inhibition is crucial for determining the steady states of the network among three qualitatively different types of behavior. Equal strength of both types of inhibitory connections leads the network to the well-known winner-take-all behavior. If, however, the lateral inhibition is weaker than the self-inhibition, a certain number of neurons are activated in the steady states or the number of winners is in general more than one (the winners-share-all behavior). On the other hand, if the self-inhibition is weaker than the lateral one, only one neuron is activated, but the winner is not necessarily the neuron receiving the largest input. It is suggested that our simple network model provides a mathematical basis for understanding neural selection mechanisms.

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

“…In simulation, they have shown that winner-takes-all like competition occurs within a single domain, while winners-share-all dynamics (multiple active neurons) occur in networks composed of multiple overlapping domains (Wickens et al, 1991;Alexander & Wickens, 1993). Similar results have been obtained in analytical studies of general mutually inhibitory neural networks (Fukai & Tanaka, 1997).…”

The basal ganglia: a vertebrate solution to the selection problem?

“…A second class of distributed selection architectures is illustrated by the network shown in Figure 3B. In architectures of this type all competitors are reciprocally connected so that each one has an inhibitory link to every otherÑan arrangement termed recurrent reciprocal inhibition 27,94 Ñand an excitatory link to the shared output resource. Such networks display a form of positive feedback since increased activity in one competitor causes increased inhibition on all others thereby reducing their inhibitory effect on the first.…”

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“…At the same time, non-winning neurons become silent due to the dynamics of the neurons in the network, not because they are algorithmically reset. Previous seminal works also studied the neural dynamics leading to emergent competition in terms of the different properties potentially involved in the process, like the strength and range of lateral inhibition [9][10][11], the value of the firing threshold [10,18] and the steepness of the activation function [18].…”