Fast convergence of spike sequences to periodic patterns in recurrent networks

Dezhe Z. Jin and H. Sebastian Seung


Dynamical attractors are thought to underlie many functions of biological neural networks. Previously, rate based models are used to prove the convergence properties of recurrent neural networks. Here we extend the attractor idea to biologically more realistic models of neural networks with neurons interacting with individual spikes rather than averaged spike rates. Specifically, we show that stable periodic spike sequences with precise timings are the attractors of the spiking dynamics in recurrent neural networks with global inhibition. Almost all spike sequences converge within a finite number of transient spikes to these attractors. The convergence is fast, especially when the global inhibition is strong. Our results support the possibility that precise spatio-temporal sequences of spikes are useful for information encoding and processing in biological neural networks.