Quantifying the separability of data classes in neural networks.

We introduce the Generalized Discrimination Value (GDV) that measures, in a non-invasive manner, how well different data classes separate in each given layer of an artificial neural network. It turns out that, at the end of the training period, the GDV in each given layer L attains a highly reproducible value, irrespective of the initialization of the network's connection weights. In the case of multi-layer perceptrons trained with error backpropagation, we find that classification of highly complex data sets requires a temporal reduction of class separability, marked by a characteristic 'energy barrier' in the initial part of the GDV(L) curve. Even more surprisingly, for a given data set, the GDV(L) is running through a fixed 'master curve', independently from the total number of network layers. Finally, due to its invariance with respect to dimensionality, the GDV may serve as a useful tool to compare the internal representational dynamics of artificial neural networks with different architectures for neural architecture search or network compression; or even with brain activity in order to decide between different candidate models of brain function.