Emergent Rate-Based Dynamics in Duplicate-Free Populations of Spiking Neurons

Can spiking neural networks (SNNs) approximate the dynamics of recurrent neural networks? Arguments in classical mean-field theory based on laws of large numbers provide a positive answer when each neuron in the network has many "duplicates", i.e., other neurons with almost perfectly correlated inputs. Using a disordered network model that guarantees the absence of duplicates, we show that duplicate-free SNNs can converge to recurrent neural networks, thanks to the concentration of measure phenomenon. This result reveals a general mechanism underlying the emergence of rate-based dynamics in large SNNs.