Beyond-mean-field theory for the statistics of neural coordination

Moritz Layer, Moritz Helias, David Dahmen
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Neurons and Cognition (q-bio.NC)
2023-07-31 16:00:00
Understanding the coordination structure of neurons in neuronal networks is essential for unraveling the distributed information processing mechanisms in brain networks. Recent advancements in measurement techniques have resulted in an increasing amount of data on neural activities recorded in parallel, revealing largely heterogeneous correlation patterns across neurons. Yet, the mechanistic origin of this heterogeneity is largely unknown because existing theoretical approaches linking structure and dynamics in neural circuits are mostly restricted to average connection patterns. Here we present a systematic inclusion of variability in network connectivity via tools from statistical physics of disordered systems. We study networks of spiking leaky integrate-and-fire neurons and employ mean-field and linear-response methods to map the spiking networks to linear rate models with an equivalent neuron-resolved correlation structure. The latter models can be formulated in a field-theoretic language that allows using disorder-average and replica techniques to systematically derive quantitatively matching beyond-mean-field predictions for the mean and variance of cross-covariances as functions of the average and variability of connection patterns. We show that heterogeneity in covariances is not a result of variability in single-neuron firing statistics but stems from the sparse realization and variable strength of connections, as ubiquitously observed in brain networks. Average correlations between neurons are found to be insensitive to the level of heterogeneity, which in contrast modulates the variability of covariances across many orders of magnitude, giving rise to an efficient tuning of the complexity of coordination patterns in neuronal circuits.
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