Communications of the ACM
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
What size net gives valid generalization?
Neural Computation
Single neuron computation
Hebbian computations in hippocampal dendrites and spines
Single neuron computation
NMDA-based pattern discrimination in a modeled cortical neuron
Neural Computation
Rigorous learning curve bounds from statistical mechanics
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Fat-shattering and the learnability of real-valued functions
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Vapnik-Chervonenkis dimension of neural networks
The handbook of brain theory and neural networks
Neural Computation
Lower bounds for the computational power of networks of spiking neurons
Neural Computation
VC dimension of an integrate-and-fire neuron model
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
On the complexity of learning for a spiking neuron (extended abstract)
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
On the relevance of time in neural computation and learning
Theoretical Computer Science
| Hi-index | 0.00 |
We compute 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 T 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 at some specified time. We show that the VC dimension diverges only logarithmically with the input signal bandwidth N. We also extend this approach to arbitrary passive dendritic trees. The main contributions of this work are (1) it offers a novel treatment of computational capacity of this class of dynamic system; and (2) it provides a framework for analyzing the computational capabilities of the dynamic systems defined by networks of spiking neurons.