Distributional properties of ReLU-activations in Artificial Neural Networks that learn by memorization

Kurzfassung

We investigate the distributional properties of layers in Artificial Neural Network (ANN) that can be used to distinguish between networks learning by generalization and memorizing networks. Starting from the notion of memorization being essentially definable as learning rare features of the input data, we propose the activation probability of Rectified Linear Units (ReLU)-neurons as an important indicator of memorization. Based on this idea, we postulate hypotheses on the activation probability and correlation structure of singular neurons in memorizing ANN and empirically evaluate them on classification tasks. We then combine these ideas with previous work on using Poisson process models of activations in ANN and extend them to consider the correlation between neurons. Using this approach, we simulate the effect of memorizing neurons on distributional properties of weight matrices and activation magnitudes. Our initial findings show how the activation frequency and intra-layer correlation structure can be used to distinguish generalizing from memorizing networks.