Introduction

Neural networks of spin glass type reveal remarkable properties of a content-addressable memory (Hopfield, 1982; Amit et al, 1985; Kinzel, 1985a). They are able to retrieve the full information of a learned pattern from an initial state which contains only partial information. Recently much effort has been devoted to the modeling of networks based on Hebb's learning rule (Cooper et al., 1979). These networks are the Hopfield model and its modifications. All have in common a local learning rule which allows the storage of orthogonal patterns without errors. The learning rule is local if the change of the synaptic coefficient depends only on the states of the two interconnected neurons and possibly on the local field of the postsynaptic one. This property seems to be essential from a biological point of view. However, the storing capability of these networks is strongly limited by the fact that they are not able to store correlated patterns without errors (Kinzel, 1985b).

On the other hand a storing procedure for correlated patterns is available (Personnaz et al, 1985; Kanter & Sompolinsky, 1986). But it involves matrix inversions which are not equivalent to a local learning mechanism. It is the purpose of this paper to present a new local learning rule for neural networks which are able to store both correlated and uncorrelated patterns. Moreover, this learning rule enables the network to fulfil two further important properties of natural networks: the learning process does not reverse the signs of the synaptic coefficients and leads to a network with unsymmetric bonds even if it starts from a symmetric one.