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Resonant spatio-temporal learning in large random recurrent networks

Emmanuel Daucé (1), Mathias Quoy (2), Bernard Doyon (3)
(1) Movement and Perception (UMR6559)
Faculty of Sport Science, University of the Mediterranean,
163, avenue de Luminy, CP 910,
13288 Marseille cedex 9, France
dauce@esm2.imt-mrs.fr
(2) Neurocybernetics team, ETIS, UCP - ENSEA
6, av. du Ponceau, 95014 Cergy-Pontoise cedex, France.
quoy@u-cergy.fr
(3) Unité INSERM U455, Service de Neurologie-CHU Purpan
31059 Toulouse cedex, France.
doyon@purpan.inserm.fr

Abstract:

Taking global analogy with the structure of perceptual biological systems, we present a system composed of two layers of continuous sigmoidal neurons. The primary layer receives stimulating spatio-temporal signals, and the secondary layer is a fully-connected random recurrent network. This secondary layer spontaneously displays complex chaotic dynamics. All connections have a constant time delay. We use for our experiments a Hebbian (covariance) learning rule. This rule slowly modifies the weights under the influence of a periodic stimulus. The effect of learning is twice : (i) it simplifies the secondary layer dynamics, which eventually stabilizes a periodic orbit, and (ii) it connects the secondary layer to the primary layer, and realizes a feedback from the secondary to the primary layer. This feedback signal is added to the incoming signal, and matches with it (i.e. the secondary layer performs a one-step prediction on the forthcoming stimulus). After learning, a resonant behavior can be observed: the system resonates with familiar stimuli, and activates a feedback signal. In particular, this resonance allows to recognize and retrieve partial signals, and to maintain in the dynamics the memory of past events. This resonance is highly sensitive to the time relationships and to the periodicity of the presented stimuli. When the presented stimulus does not match in time or space, the feedback remains silent. The number of different stimuli for which resonant behavior can be learned is analyzed. As with Hopfield networks, the capacity is proportional to the size of the second, recurrent layer. Moreover, the high capacity displayed allows to consider the implementation of our model on real-time systems interacting with their environment. Such an implementation is reported in the case of a simple behavior-based recognition task on a mobile robot. At last, we present some functional analogies with biological systems in terms of autonomy and dynamical binding, and present some hypotheses on the computational role of feedback connections.

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