On the Complexity of Training a Single Perceptron with Programmable Synaptic Delays
Author: Jirí Síma.
Source: Lecture Notes in Artificial Intelligence Vol. 2842, 2003, 221 - 233.
Abstract. We consider a single perceptron with synaptic delays which generalizes a simplified model for a spiking neuron where not only the time that a pulse needs to travel through a synapse is taken into account but also the input firing rates may have more different levels. A synchronization technique is introduced so that the results concerning the learnability of spiking neurons with binary delays also apply to with arbitrary delays. In particular, the consistency problem for with programmable delays and its approximation version prove to be NP-hard. It follows that the perceptrons with programmable synaptic delays are not properly PAC-learnable and the spiking neurons with arbitrary delays do not allow robust learning unless RP = NP. In addition, we show that the representation problem for which is an issue whether an n-variable Boolean function given in DNF (or as a disjunction of O(n) threshold gates) can be computed by a spiking neuron is co-NP-hard.
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