Theory of Communication Subspaces for Stochastic Recurrent Neural Networks

The brain relies on communication between specialized cortical areas to accomplish complex cognitive tasks. To fully understand and replicate this ability of the brain in artificial systems, we need a deeper understanding of information transfer across cortical areas. We reduce this gap by developing analytical tools to analyze interareal communication in terms of coherence and noise correlations in subpopulations of neurons within and across areas. We take a dynamical systems approach in designing stable stochastic network architectures yielding systems that display features characteristic of neuronal networks. We then show that for a rather broad class of systems we can derive analytical expressions for correlations, power spectra, and coherence. Based on this analysis, we derive a theory that predicts the emergence of communication subspaces as a mechanism for interareal communication, as observed in recent experiments. We illustrate these approaches for two distinct types of circuit models: 1) A dynamically stable stochastic recurrent convolutional neural network trained on image datasets; and 2) A stochastic recurrent circuit implementing divisive normalization, where the responses of neurons are divided by a weighted sum of the activity of a population of neurons.