Some Theoretical Properties of a Network of Discretely Firing Neurons

TL;DR

This paper explores the theoretical properties of discretely firing neuron networks, introducing an objective function for optimal encoding, leading to insights like topographic mappings and factorial encoder networks.

Contribution

It presents a novel objective function for optimizing discretely firing neuron networks and derives key properties such as topographic mappings and factorial encoders.

Findings

Minimizing the objective function leads to topographic mappings.

Firing probability depends piecewise linearly on input.

Networks can function as factorial encoders.

Abstract

The problem of optimising a network of discretely firing neurons is addressed. An objective function is introduced which measures the average number of bits that are needed for the network to encode its state. When this is minimised, it is shown that this leads to a number of results, such as topographic mappings, piecewise linear dependence on the input of the probability of a neuron firing, and factorial encoder networks.