VC DIMENSION OF AN INTEGRATE-AND-FIRE NEURON MODEL

We compute the VC dimension of a leaky integrate-and-fire neuron model . The VC dimension quantifies the ability of a function class to parti tion an input pattern space, and can be considered a measure of comput ational capacity. In this case, the function class is the class of int egrate-and-fire models generated by varying the integration time const ant tau and the threshold theta, the input space they partition is the space of continuous-time signals, and the binary partition is specifi ed by whether or not the model reaches threshold at some specified tim e. We show that the VC dimension diverges only logarithmically with th e input signal bandwidth N. We also extend this approach to arbitrary passive dendritic trees. The main contributions of this work are (1) i t offers a novel treatment of computational capacity of this class of dynamic system; and (2) it provides a framework for analyzing the comp utational capabilities of the dynamic systems defined by networks of s piking neurons.