Decorrelating neurons using persistence

TL;DR

This paper introduces a novel regularisation method based on topological persistence to decorrelate neurons in deep networks, improving generalisation by reducing redundancy.

Contribution

It presents the first differentiable topological persistence-based regularisation terms for neural networks, outperforming traditional correlation minimisation methods.

Findings

Our regularisers outperform popular correlation-based regularisation methods.

Naive correlation minimisation results in lower accuracy, highlighting the importance of redundancy.

The method is applicable to various deep learning tasks, including classification, generation, and regression.

Abstract

We propose a novel way to improve the generalisation capacity of deep learning models by reducing high correlations between neurons. For this, we present two regularisation terms computed from the weights of a minimum spanning tree of the clique whose vertices are the neurons of a given network (or a sample of those), where weights on edges are correlation dissimilarities. We provide an extensive set of experiments to validate the effectiveness of our terms, showing that they outperform popular ones. Also, we demonstrate that naive minimisation of all correlations between neurons obtains lower accuracies than our regularisation terms, suggesting that redundancies play a significant role in artificial neural networks, as evidenced by some studies in neuroscience for real networks. We include a proof of differentiability of our regularisers, thus developing the first effective topological persistence-based regularisation terms that consider the whole set of neurons and that can be applied to a feedforward architecture in any deep learning task such as classification, data generation, or regression.