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.

5 pages, 2 figures, Accepted (Physical Review Letters)

References in corpus (2)

• Extensive load in multitasking associative networks
• Correlated fluctuations in strongly-coupled binary networks beyond equilibrium

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