Noisy Spiking Neurons with Temporal Coding have more Computational Power than Sigmoidal Neurons

Part of Advances in Neural Information Processing Systems 9 (NIPS 1996)

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Authors

Wolfgang Maass

Abstract

We exhibit a novel way of simulating sigmoidal neural nets by net(cid:173) works of noisy spiking neurons in temporal coding. Furthermore it is shown that networks of noisy spiking neurons with temporal coding have a strictly larger computational power than sigmoidal neural nets with the same number of units.

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Introduction and Definitions

We consider a formal model SNN for a Ā§piking neuron network that is basically a reformulation of the spike response model (and of the leaky integrate and fire model) without using 6-functions (see [Maass, 1996a] or [Maass, 1996b] for further backgrou nd).

An SNN consists of a finite set V of spiking neurons, a set E ~ V x V of synapses, a weight wu,v 2: 0 and a response function cu,v : R+ --+ R for each synapse {u, v} E E (where R+ := {x E R: x 2: O}) , and a threshold function 8 v : R+ --+ R+ for each neuron v E V .

If Fu ~ R+ is the set of firing times of a neuron u , then the potential at the trigger zone of neuron v at time t is given by