Abstract
We derive macroscopic Lyapunov functions for large, long-range, Ising-spin neural networks with separable symmetric interactions, which evolve in time according to local field alignment. We generalize existing constructions, which correspond todeterministic (zero-temperature) evolution and to specific choices of the interaction structure, to the case ofstochastic 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.
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Laughton, S.N., Coolen, A.C.C. Macroscopic Lyapunov functions for separable stochastic neural networks with detailed balance. J Stat Phys 80, 375–387 (1995). https://doi.org/10.1007/BF02178364
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DOI: https://doi.org/10.1007/BF02178364