# Linking structure and activity in nonlinear spiking networks

arXiv: https://arxiv.org/abs/1610.03828 · HTML: https://mlsanity.com/paper/1610.03828/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2016.

## Built on by (most cited first, 2 of 2)

- [An algorithm for the computation of joint Hawkes moments with exponential kernel](https://mlsanity.com/paper/2110.13649/) (2021)
- [Motif distribution and function of sparse deep neural networks](https://mlsanity.com/paper/2403.00974/) (2024)

## Abstract (arXiv)

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.