A BAYESIAN INTERPRETATION FOR THE EXPONENTIAL CORRELATION ASSOCIATIVEMEMORY

The exponential correlation associative memory (ECAM) is a recurrent n eural network model which has large storage capacity and is particular ly suited for VLSI hardware implementation. Our aim in this paper is t o show how the ECAM model can be entirely derived within a Bayesian fr amework, thereby providing more insight into the behaviour of this alg orithm. The framework for our study is a novel relaxation method which involves direct probabilistic modelling of the pattern corruption mec hanism. The parameter of this model is the memoryless probability of e rror on nodes of the network. This bit-error probability is not only i mportant for the interpretation of the ECAM model, but allows also us to understand some more general properties of Bayesian pattern reconst ruction by relaxation. In addition, we demonstrate that both the Hopfi eld memory and the Boolean network model developed by Aleksander can b e regarded as limits of the presented relaxation approach with precise physical meaning in terms of this parameter. To study the dynamical b ehaviour of our relaxation model, we use the Hamming distance picture of Kanerva which allows us to understand how the bit-error probability evolves during the relaxation process. We also derive a parameter-fre e expression for the storage capacity of the model which, like a previ ous result of Chiueh and Goodman, scales exponentially with the number of nodes in the network. (C) 1998 Elsevier Science B.V. All rights re served.