Spectral Analysis of Latent Representations

We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers. Saturation is based on spectral analysis and can be computed efficiently, making live analysis of the representations practical during training. We provide an outlook for future applications of this metric by outlining the behaviour of layer saturation in different neural architectures and problems. We further show that saturation is related to the generalization and predictive performance of neural networks.