[Selective stabilization of neuronal representations by resonance between spontaneous prerepresentations of the cerebral network and percepts evoked by interaction with the outside world].

Changeux et al. (Changeux, Heidmann and Patte, in "The Biology of Learning" Dahlem Conference, 1984, pp. 115-133, Springer Verlag) have recently discussed a model of "learning by selection" in which the storage of patterns of activity--or prerepresentations--within a network of neurons, results from the coincidence or "resonance" between a spontaneous activity of the neurons and external signals applied to the network--for instance sensory stimuli. In this Note, a mathematical formulation of the model is presented, based on that proposed by Little and Shaw (Little, Math. Biosci., 19, 1974, pp. 101-120; Little and Shaw, Math. Biosci., 39, 1978, pp. 281-290) for the statistical analysis of neuronal activity within a network, and on a rule for modulation of synaptic efficacies derived from that proposed by Hebb (Hebb, The Organisation of Behaviour, 1949, Wiley). The effect of an external signal sigma on the probability P(beta) of occurrence of a given prerepresentation beta under stationary conditions has been analytically derived [cf. equation (16) in text]. Taking into account that the system spontaneously fluctuates between various prerepresentations, it is shown that P(beta) is increased by the external signal sigma when (1) beta is close to sigma--namely the external signal significantly modifies the probabilities of those prerepresentations that resemble sigma--, and (2) when the external signal sigma sets the neurons precisely in the state that they would have more probably reached at the moment when the external signal was applied. Namely there should exist a "resonance" between sigma and the prerepresentation of the network when sigma is applied.