Finite Size Effects in Separable Recurrent Neural Networks

Details Finite Size Effects in Separable Recurrent Neural Networks Finite Size Effects in Separable Recurrent Neural Networks

1998-03-31

arxiv.org/abs/cond-mat/9803386v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages LaTex, with 4 postscript figures included

Scientific paper

10.1088/0305-4470/31/31/009

We perform a systematic analytical study of finite size effects in separable recurrent neural network models with sequential dynamics, away from saturation. We find two types of finite size effects: thermal fluctuations, and disorder-induced `frozen' corrections to the mean-field laws. The finite size effects are described by equations that correspond to a time-dependent Ornstein-Uhlenbeck process. We show how the theory can be used to understand and quantify various finite size phenomena in recurrent neural networks, with and without detailed balance.

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