A complete mean-field theory for dynamics of binary recurrent neural networks
Abstract
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description of nonequilibrium fluctuations in networks with finite size and finite degree of interactions. Our approach allows the investigation of systems for which a deterministic mean-field theory breaks down. To demonstrate this, we uncover a novel dynamic state in which a recurrent network of binary units with statistically inhomogeneous interactions, along with an asynchronous behavior, also exhibits collective nontrivial stochastic fluctuations in the thermodynamical limit.
Keywords
Cite
@article{arxiv.1701.07128,
title = {A complete mean-field theory for dynamics of binary recurrent neural networks},
author = {Farzad Farkhooi and Wilhelm Stannat},
journal= {arXiv preprint arXiv:1701.07128},
year = {2017}
}
Comments
5 pages, 2 figures, Accepted (Physical Review Letters)