Theory of spike timing based neural classifiers

TL;DR

This paper analyzes the Tempotron neuron model's ability to classify spike sequences, deriving its capacity using statistical mechanics, and reveals its solution space structure and capacity limits.

Contribution

It provides a theoretical analysis of the Tempotron's computational capacity and solution space structure, extending understanding beyond static perceptrons.

Findings

Tempotron's capacity per synapse is finite and scales weakly with stimulus duration.

Solution space consists of many small clusters of weight vectors.

Capacity analysis uses statistical mechanics and extreme value theory.

Abstract

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.