Competitive learning behavior in a stochastic neural network

Stochastic behavior is a natural and inevitable property of biological neurons. The effect of stochastic behavior or thermal fluctuation in neural firings on the learning process in a neural system is investigated. A learning model, which is derived from the stochastic differential equation of the firing-rate model, is presented as an estimate of the gradient flow of free energy. The model reveals that the learning process becomes competitive owing to the effect of entropy even through the synapse modifications only follow the simple Hebbian rule.