Embedding Complexity of Learned Representations in Neural Networks

Abstract

In classification tasks, the set of training examples for each class can be viewed as a limited sampling from an ideal infinite manifold of all sensible representants of this class. A layered artificial neural network model trained for such a task can then be interpreted as a stack of continuous transformations which gradually mold these complex manifolds from the original input space to simpler dissimilar internal representations on successive hidden layers – the so-called manifold disentaglement hypothesis. This, in turn, enables the final classification to be made in a linear fashion. We propose to assess the extent of this separation effect by introducing a class of measures based on the embedding complexity of the internal representations, with evaluation of the KL-divergence of t-distributed stochastic neighbour embedding (t-SNE) appearing as the most suitable method. Finally, we demonstrate the validity of the disentanglement hypothesis by measuring embedding complexity, classification accuracy and their relation on a sample of image classification datasets.