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