Zador, Anthony M. and Pearlmutter, Barak A. (1999) VC Dimension of an Integrate-and-Fire Neuron Model. In: COLT '96: ninth annual conference on Computational learning theory, June 28-July 1, 1996, Desenzano del Garda, Italy.

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Abstract

We find the VC dimension of a leaky integrate-and-fire neuron model. The VC dimension quantifies the ability of a function class to partition an input pattern space, and can be considered a measure of computational capacity. In this case, the function class is the class of integrate-and-fire models generated by varying the integration time constant τ and the threshold ϴ, the input space they partition is the space of continuous-time signals, and the binary partition is specified by whether or not the model reaches threshold and spikes at some specified time. We show that the VC dimension diverges only logarithmically with the input signal bandwidth N , where the signal bandwidth is determined by the noise inherent in the process of spike generation. For reasonable estimates of the signal bandwidth, the VC dimension turns out to be quite small (¡10). We also extend this approach to ar- bitrary passive dendritic trees. The main contributions of this work are (1) it offers a novel treatment of the computational capacity of this class of dynamic system; and (2) it provides a framework for analyzing the computational capabilities of the dynamical systems defined by networks of spiking neurons.

Item Type:	Conference or Workshop Item (Paper)
Keywords:	VC Dimension; Integrate-and-Fire Neuron Model;
Academic Unit:	Faculty of Science and Engineering > Computer Science
Item ID:	8132
Depositing User:	Barak Pearlmutter
Date Deposited:	07 Apr 2017 15:36
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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