Effects of Fast Presynaptic Noise in Attractor Neural Networks

Abstract

We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological findings that show that synaptic strength may either increase or decrease on a short timescale depending on presynaptic activity. We thus describe a mechanism by which fast presynaptic noise enhances the neural network sensitivity to an external stimulus. The reason is that, in general, presynaptic noise induces nonequilibrium behavior and, consequently, the space of fixed points is qualitatively modified in such a way that the system can easily escape from the attractor. As a result, the model shows, in addition to pattern recognition, class identification and categorization, which may be relevant to the understanding of some of the brain complex tasks.

Chaotic hopping between attractors in neural networks

“…Our system reduces to the Hopfield case with Little dynamics (parallel updating) only for Φ = −1. Our main result is that, as described in detail in the previous section, the automaton eventually exhibits chaotic behavior for Φ = −1, but not for Φ = −1, nor in the case of sequential, single-neuron updating irrespective of the value of Φ (Cortes et al, 2006). It also follows from our analysis above that further study of this system and related automata is needed in order to determine other conditions for chaotic hopping.…”

“…Interesting enough, concerning this property, neural automata often exhibit more interesting behavior than their Hopfield-like, sequentially-updated counterparts, in spite of the fact that any two successive states are stronger correlated in the sequential case. Therefore, we extend here to cellular automata our recent study of the effects of synaptic "noise" on the stability of attractors in Hopfield-like networks (Cortes et al, 2006). We demonstrate that, in our automaton, a certain type of synaptic fluctuations determine an interesting retrieval process.…”

“…It is obvious that the above may be adapted to cover other, more involved cases (Cortes et al, 2006), but this is enough to our purposes here. In fact, Monte Carlo simulations reveal some new interesting facts as compared with the case of sequential updating (Cortes et al, 2006).…”

“…Interesting enough, (3) clearly induces some non-trivial correlations between synaptic noise and neural activity. This is an additional bonus of our choice, as it conforms the general expectation that processing of information in a network will depend on the noise affecting the communication lines and vice versa (Cortes et al, 2006). Looking for an increasing function of the total presynaptic current with proper normalization, a simple choice for the probability in (3) is ζ ( m) = (1 + α)…”

Instabilities in attractor networks with fast synaptic fluctuations and partial updating of the neurons activity

“…In this note we show that such a limitation may be systematically overcome by simply generalizing familiar model situations. More specifically, we here extend some of our recent work on ANN with fast pre-synaptic noise (Cortes et al, 2006;Torres et al, 2007;Marro et al, 2007). The result is a novel mathematically-tractable ANN whose activity eventually describes heteroclinic paths among the attractors.…”