Linking structure and activity in nonlinear spiking networks

TL;DR

This paper develops a new theoretical framework using statistical field theory to relate neural connectivity and activity in nonlinear spiking networks, overcoming limitations of linear approximations.

Contribution

It introduces a diagrammatic fluctuation expansion that captures nonlinear responses and higher-order correlations in neural networks, linking structure to activity more accurately.

Findings

Recurrent network structure produces pairwise and higher-order correlations.

Nonlinearities significantly influence spiking activity.

The framework enables analysis of how cell-type nonlinearities shape population activity.

Abstract

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of {\it structure-driven activity} has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities---including those of different cell types---combine with connectivity to shape population activity and function.