Neuronal Correlation: a Central Concept in Neural Network

TL;DR

This paper introduces neuronal correlation as a key concept in neural networks, demonstrating its role in network generalization, entropy estimation accuracy, and proposing a novel method to compute entropy considering neuronal correlation.

Contribution

The paper establishes neuronal correlation as a central measure in neural networks and presents a new entropy estimation method that accounts for neuronal correlation.

Findings

Neuronal correlation can be efficiently estimated via weight matrices.

Enforcing neuronal correlation improves network generalization.

Considering neuronal correlation enhances entropy estimation accuracy.

Abstract

This paper proposes to study neural networks through neuronal correlation, a statistical measure of correlated neuronal activity on the penultimate layer. We show that neuronal correlation can be efficiently estimated via weight matrix, can be effectively enforced through layer structure, and is a strong indicator of generalisation ability of the network. More importantly, we show that neuronal correlation significantly impacts on the accuracy of entropy estimation in high-dimensional hidden spaces. While previous estimation methods may be subject to significant inaccuracy due to implicit assumption on neuronal independence, we present a novel computational method to have an efficient and authentic computation of entropy, by taking into consideration the neuronal correlation. In doing so, we install neuronal correlation as a central concept of neural network.