Pattern recognition minimizes entropy production in a neural network of electrical oscillators

Abstract

Abstract We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Holzel and Krischer, 2011 [13] ). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈 d S / d t 〉 of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈 d S / d t 〉 is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.