Non-perturbative renormalization group analysis of strongly-coupled spiking networks

To fully explain how neural dynamics transmit information and perform computations, we need to understand the structure of the coordinated activity of neurons and their responses to external inputs. Given a model of neural dynamics and their synaptic connections, we would in principle achieve this goal by calculating the statistical and response functions of the network---a notoriously intractable task for all but the simplest models. While diagrammatic series have been successfully used to correct mean field predictions in weakly-coupled network models, they break down in networks with strong nonlinear behavior, demanding new approximation methods.

Here, we employ ``non-perturbative renormalization group'' methods to analyze strongly-coupled spiking networks. We show that the true mean firing rates of the network satisfy a nonlinear system of equations formally similar to the mean-field system but with a different effective nonlinearity. We explicitly derive a differential equation for this nonlinearity and solve it numerically. Our results predict the distribution of firing rates in simulated networks of neurons reasonably well, even in strong coupling regimes in which perturbative calculations begin to break down.