Understanding spiking networks through convex optimization

Neurons mainly communicate through spikes, and much effort has been spent to understand how the dynamics of spiking neural networks (SNNs) relates to their connectivity. Meanwhile, most major advances in machine learning have been made with simpler, rate-based networks, with SNNs only recently showing competitive results, largely thanks to transferring insights from rate to spiking networks. However, it is still an open question exactly which computations SNNs perform. Recently, the time-averaged firing rates of several SNNs were shown to yield the solutions to convex optimization problems. Here we turn these findings around and show that virtually all inhibition-dominated SNNs can be understood through the lens of convex optimization, with network connectivity, timescales, and firing thresholds being intricately linked to the parameters of underlying convex optimization problems.