• Abstract: We propose a new notion of 'non-linearity' of a network layer with respect to an input batch that is based on its proximity to a linear system, which is reflected in the non-negative rank of the activation matrix. We measure this non-linearity by applying non-negative factorization to the activation matrix. Considering batches of similar samples, we find that high non-linearity in deep layers is indicative of memorization. Furthermore, by applying our approach layer-by-layer, we find that the mechanism for memorization consists of distinct phases. We perform experiments on fully-connected and convolutional neural networks trained on several image and audio datasets. Our results demonstrate that as an indicator for memorization, our technique can be used to perform early stopping.
• Keywords: Memorization, Generalization, ReLU, Non-negative matrix factorization
• TL;DR: We use the non-negative rank of ReLU activation matrices as a complexity measure and show it (negatively) correlates with good generalization.