Spontaneous Dynamics and Associative Learning in an Assymetric Recurrent Random Neural Network

Abstract

Freeman’s investigations on the olfactory bulb of the rabbit showed that its dynamics was chaotic, and that recognition of a learned pattern is linked to a dimension reduction of the dynamics on a much simpler attractor (near limit cycle). We adress here the question wether this behaviour is specific of this particular architecture or if this kind of behaviour observed is an important property of chaotic neural network using a Hebb- like learning rule. In this paper, we use a mean-field theoretical statement to determine the spontaneous dynamics of an assymetric recurrent neural network. In particular we determine the range of random weight matrix for which the network is chaotic. We are able to explain the various changes observed in the dynamical regime when sending static random patterns. We propose a Hebb-like learning rule to store a pattern as a limit cycle or strange attractor. We numerically show the dynamics reduction of a finite-size chaotic network during learning and recognition of a pattern. Though associative learning is actually performed the low storage capacity of the system leads to the consideration of more realistic architecture.