Networks of spiking neurons that compute linear functions using action potential timing

Berthold Ruf

doi:10.1117/12.343071

22 March 1999 Networks of spiking neurons that compute linear functions using action potential timing

Berthold Ruf

Proceedings Volume 3728, Ninth Workshop on Virtual Intelligence/Dynamic Neural Networks; (1999) https://doi.org/10.1117/12.343071
Event: Ninth Workshop on Virtual Intelligence/Dynamic Neural Networks: Neural Networks Fuzzy Systems, Evolutionary Systems and Virtual Re, 1998, Stockholm, Sweden

Abstract

For fast neural computations within the brain it is very likely that the timing of single firing events is relevant. Recently Maass has shown that under certain weak assumptions a weighted sum can be computed in temporal coding by leaky integrate-and-fire neurons. This construction can be extended to approximate arbitrary functions. In comparison to integrate-and-fire neurons there are several sources in biologically more realistic neurons for additional nonlinear effects like e.g. the spatial and temporal interaction of postsynaptic potentials or voltage-gated ion channels at the soma. Here we demonstrate with the help of computer simulations using GENESIS that despite of these nonlinearities such neurons can compute linear functions in a natural and straightforward way based on the main principles of the construction given by Maass. One only has to assume that a neuron receives all its inputs in a time interval of approximately the length of the rising segment of its excitatory postsynaptic potentials. We also show that under certain assumptions there exists within this construction some type of activation function being computed by such neurons. Finally we demonstrate that on the basis of these results it is possible to realize in a simple way pattern analysis with spiking neurons. It allows the analysis of a mixture of several learned patterns within a few milliseconds.

Citation Download Citation

Berthold Ruf "Networks of spiking neurons that compute linear functions using action potential timing", Proc. SPIE 3728, Ninth Workshop on Virtual Intelligence/Dynamic Neural Networks, (22 March 1999); https://doi.org/10.1117/12.343071

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KEYWORDS

Neurons

Biological research

Samarium

Sensors

Computer simulations

Action potentials

Systems modeling

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