The Impact of Activation Sparsity on Overfitting in Convolutional Neural Networks

Overfitting is one of the fundamental challenges when training convolutional neural networks and is usually identified by a diverging training and test loss. The underlying dynamics of how the flow of activations induce overfitting is however poorly understood. In this study we introduce a perplexity-based sparsity definition to derive and visualise layer-wise activation measures. These novel explainable AI strategies reveal a surprising relationship between activation sparsity and overfitting, namely an increase in sparsity in the feature extraction layers shortly before the test loss starts rising. This tendency is preserved across network architectures and reguralisation strategies so that our measures can be used as a reliable indicator for overfitting while decoupling the network's generalisation capabilities from its loss-based definition. Moreover, our differentiable sparsity formulation can be used to explicitly penalise the emergence of sparsity during training so that the impact of reduced sparsity on overfitting can be studied in real-time. Applying this penalty and analysing activation sparsity for well known regularisers and in common network architectures supports the hypothesis that reduced activation sparsity can effectively improve the generalisation and classification performance. In line with other recent work on this topic, our methods reveal novel insights into the contradicting concepts of activation sparsity and network capacity by demonstrating that dense activations can enable discriminative feature learning while efficiently exploiting the capacity of deep models without suffering from overfitting, even when trained excessively.