Associative memories: randomness, continuity and biological plausibility

Abstract

A new, biologically plausible model of associative memory is presented. First, a historical perspective of the more relevant improvements to the basic Little-Hopfield model is given. Then, we introduce a stochastic system with graded response neurons and a network consisting of a non countable number of neurons organized in a continuous metric space. We do this by casting the retrieval process of an analog Hopfield model [7] into the framework of a diffusive process governed by the Fokker-Plank (F-P) equation. This model has the ability to escape spurious memories and, at the same time, is continuous in neural transfer function, topology and time scale. However, it requires the use of path integrals on functional, infinite dimensional spaces, thus turning very difficult any further analytical treatment. Then we resign the continuous topological description of the state space, unifying the graded response units model [7] and the stochastic approach, and obtaining a complete description of the retrieval process at both the microscopic, individual neuron level and the macroscopic level of time evolution of the probability density function over the space of all possible activation patterns.