  We propose a probe for the analysis of deep learning architectures that is
based on machine learning and approximation theoretical principles. Given a
deep learning architecture and a training set, during or after training, the
Sparsity Probe allows to analyze the performance of intermediate layers by
quantifying the geometrical features of representations of the training set. We
show how the Sparsity Probe enables measuring the contribution of adding depth
to a given architecture, to detect under-performing layers, etc., all this
without any auxiliary test data set.
