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Название: Macroscopic Lyapunov Functions for Separable Stochastic Neural Networks with Detailed Balance
Авторы: Laughton S.N., Coolen A.C.C.
We derive macroscopic Lyapunov functions for large, long-range, lsing-spin neural networks with separable symmetric interactions, which evolve in time according to local field alignment. We generalize existing constructions, which correspond to determfllistic (zero-temperature) evolution and to specific choices of the interaction structure, to the case of stochastic evolution and arbitrary separable interaction matrices, for both parallel and sequential spin updating. We find a direct relation between the form of the Lyapunov functions (which describe dynamical processes) and the saddle-point integration that results from performing equilibrium statistical mechanical studies of the present type of model.