Abstract
A Volterra-like polynomial representation is derived and its convergence discussed for two neuronal models in which subthreshold inputs are integrated either without loss (integrate and fire) or with a decay which follows an exponential time course (leaky integrator). This polynomial representation provides a kind of “nonlinear transfer function” for the nonlinear encoding process. Standard formulae are used to derive explicitely the output for various inputs as in linear system theory. Moreover, the nonlinear transfer function associated with cascades or networks of neurons can be also obtained. Finally, extensions and implications of these results are discussed.
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Poggio, T., Torre, V. A Volterra representation for some neuron models. Biol. Cybern. 27, 113–124 (1977). https://doi.org/10.1007/BF00337263
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DOI: https://doi.org/10.1007/BF00337263