Information space dynamics for neural networks

Abstract

We propose a coupled map lattice defined on a hypercube in M dimensions, the information space, to model memory retrieval by a neural network. We consider that both neuronal activity and the spiking phase may carry information. In this model the state of the network at a given time t is completely determined by a function y(σ,t) of the bit strings σ=(σ1, σ2 , . . . ,σM), where σi=±1 with i=1,2, . . . ,M, that gives the intensity with which the information σ is being expressed by the network. As an example, we consider logistic maps, coupled in the information space, to describe the evolution of the intensity function y(σ,t). We propose an interpretation of the maps in terms of the physiological state of the neurons and the coupling between them, obtain Hebb-like learning rules, show that the model works as an associative memory, numerically investigate the capacity of the network and the size of the basins of attraction, and estimate finite size effects. We finally show that the model, when exposed to sequences of uncorrelated stimuli, shows recency and latency effects that depend on the noise level, delay time of measurement, and stimulus intensity.