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We study generalization in deep learning by appealing to complexity measuresoriginally developed in approximation and information theory. While theseconcepts are challenged by the high-dimensional and data-defined nature of deeplearning, we show that simple vector quantization approaches such as PCA, GMMs,and SVMs capture their spirit when applied layer-wise to deep extractedfeatures giving rise to relatively inexpensive complexity measures thatcorrelate well with generalization performance. We discuss our results in 2020NeurIPS PGDL challenge.

Predicting Generalization in Deep Learning via Local Measures of Distortion