Part of Advances in Neural Information Processing Systems 6 (NIPS 1993)
A.C.C. Coolen, R. Penney, D. Sherrington
A simple model of coupled dynamics of fast neurons and slow inter(cid:173) actions, modelling self-organization in recurrent neural networks, leads naturally to an effective statistical mechanics characterized by a partition function which is an average over a replicated system. This is reminiscent of the replica trick used to study spin-glasses, but with the difference that the number of replicas has a physi(cid:173) cal meaning as the ratio of two temperatures and can be varied throughout the whole range of real values. The model has inter(cid:173) esting phase consequences as a function of varying this ratio and external stimuli, and can be extended to a range of other models.
1 A SIMPLE MODEL WITH FAST DYNAMIC
NEURONS AND SLOW DYNAMIC INTERACTIONS
As the basic archetypal model we consider a system of Ising spin neurons (J'i E {-I, I}, i E {I, ... , N}, interacting via continuous-valued symmetric interactions, Iij, which themselves evolve in response to the states of the neurons. The neurons are taken to have a stochastic field-alignment dynamics which is fast compared with the evolution rate of the interactions hj, such that on the time-scale of Iii-dynamics the neurons are effectively in equilibrium according to a Boltzmann distribution,