CTN: Christian Machens

Title: Computing with spikes: A geometric approach

Abstract: How can recurrent spiking networks perform computations in a biologically realistic regime? I will outline the progress we have made in answering this question. Our approach follows two principles. First, we don’t average over spikes, but focus on the contribution of each individual spike. Second, we study the decision to spike in a low-dimensional space of latent population modes (or readouts, components, factors, you name it) rather than in the original neural space. Neural thresholds then become convex boundaries in latent space, and the latent dynamics is either attracted (I population) or repelled (E population) by these boundaries. The combination of E and I populations results in balanced, inhibition-stabilized networks which are capable of producing (arbitrary) dynamical systems or input-output mappings. Moreover, there are profound differences between computation in these spiking networks compared to classical rate networks. I will illustrate all of these insights through geometrical pictures and movies and thereby demonstrate that we are far from having exhausted analytical and geometric methods in understanding recurrent spiking neural networks [joint work with William Podlaski].