A complete mean-field theory for dynamics of binary recurrent neural networks

Farzad Farkhooi; Wilhelm Stannat

doi:10.1103/physrevlett.119.208301

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arXiv · 1701.07128

A complete mean-field theory for dynamics of binary recurrent neural networks

Farzad Farkhooi·Wilhelm Stannat

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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.

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Farzad Farkhooi, Wilhelm Stannat. 2017-10-17. A complete mean-field theory for dynamics of binary recurrent neural networks. https://doi.org/10.1103/physrevlett.119.208301

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