Neural networks with fast time-variation of synapses

Abstract

Abstract. We study a kinetic neural network in which the intensity of synaptic couplings varies on a timescale of order p(1 − p) −1 compared with that for neuron variations. We describe some exact and mean-field results for p → 0. This includes, for example, the Hopfield model with random fluctuations of synapse intensities such that neurons couple each other, on average, according to the Hebbian learning rule. The consequences of such fluctuations on the performance of the network are analysed in detail for some specific choices of the rate and fluctuation distribution, including the case in which couplings are asymmetric.

Nonequilibrium neural network with competing dynamics

“…Also remarkable is the result that we report in Fig. 3, which is also fully consistent with our Monte Carlo observations [16]. The solutions (10) correspond, in general, to a saddle point whose details strongly depend on , so that speciÿc analysis are required.…”

“…It is likely that a similar conclusion, which one expects to hold beyond the Hopÿeld-model scenario, applies also to the behavior of biological systems. We report in this paper on the most general results from our study; further technical details and related numerical work are to be reported elsewhere [16].…”

Algorithms for identification and categorization

“…This was first studied in some detail in Refs. [17,18], and analysis of the intriguing behavior this may show concerning recognition was first reported in Refs. [19,20].…”

Chaotic hopping between attractors in neural networks

“…This situation has been formally discussed in detail in Refs. (Torres et al, 1997;Marro and Dickman, 1999). It may be noticed that, consistently with the choice of a binary, ±1 code for the neurons activity, we are assuming zero thresholds, θ i = 0, ∀i, in the following; this is relevant when comparing this work with some related one, as discussed below.…”