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Fast convergence of spike sequences to periodic patterns in recurrent
networks
Dezhe Z. Jin and H. Sebastian Seung
MIT
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.