Notions of Associative Memory and Sparse Coding.

This paper summarizes associative memory models and sparse representation of memory in these models. Important properties of the associative memory models are their storage capacity, basin of attraction, and the existence of spurious memories. Sparse coding and nonmonotonic output functions are proposed to improve them. Sparsely coded associative memory model has an extremely large storage capacity which diverges as the mean firing rate of memory patterns approaches 0. The storage capacity strongly depends on the shape of the output function as well as the mean firing rate, even in the case of monotonic output functions. Dynamical properties of the model are analyzed by means of a statistical neurodynamical method. We emphasize the necessity of a feedback mechanism to control the mean firing rate in the recall process. Recently, there have been some experimental results suggesting its existence in the brain. On the other hand, it has been shown that the storage capacity can be markedly improved by replacing the usual monotonic output function with a nonmonotonic one. Another remarkable property of the model with the nonmonotonic neurons is that it seems to have no, or almost no, spurious memory. An associative memory model using nonmonotonic modules with a feedforward inhibition is discussed. The modules consist of two types of threshold units, each of which has a different threshold and can be considered as a biologically plausible representation of the nonmonotonic output function. The above model is compared with the monotonic one. The difference in the storage capacity between the two models becomes small when the sparse patterns are stored. Finally, we discuss the biological plausibility of the discussed associative memory models and sparse coding. Copyright 1996 Elsevier Science Ltd.