Storage capacity of the exponential correlation associative memory

Abstract

In this paper we analyze the pattern storage capacity of the exponential correlation associative memory(ECAM). This architecture was first studied by Chiueh and Goodman [3] who concluded that, under certain conditions on the input patterns, the memory has a storage capacity that was exponential in the length of the bit-patterns. A recent analysis by Pelillo and Hancock [9], using the Kanerva picture of recall, concluded that the storage capacity was limited by 2^N−1/N ². Both of these analyses can be criticised on the basis that they overlook the role of initial bit-errors in the recall process and deal only with the capacity for perfect pattern recall. In other words, they fail to model the effect of presenting corrupted patterns to the memory. This can be expected to lead to a more pessimistic limit. Here we model the performance of the ECAM when presented with corrupted input patterns. Our model leads to an expression for the storage capacity of the ECAM both in terms of the length of the bit-patterns and the probability of bit-corruption in the original input patterns. These storage capacities agree closely with simulation. In addition, our results show that slightly superior performance can be obtained by selecting an optimal value of the exponential constant.