Multiplicatively interacting point processes and applications to neural modeling
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We introduce a nonlinear modification of the classical Hawkes process allowing inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for recurrent networks of spiking neurons described as Wiener cascades with exponential transfer function. The expected rates of all neurons in the network are approximated by a first-order differential system. We study the stability of the solutions of this equation, and use the new formalism to implement a winner-takes-all network that operates robustly for a wide range of parameters. Finally, we discuss relations with the generalised linear model that is widely used for the analysis of spike trains.
KeywordsPoisson process Spiking neuron Interacting random process Recurrent network dynamics Generalised linear model Winner-takes-all
We wish to thank an anonymous reviewer of the paper for discovering a flaw in our derivation of the master equation, and for suggesting the appropriate correction.
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