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Establishing associations between the structure and the generalisationability of deep neural networks (DNNs) is a challenging task in modern machinelearning. Producing solutions to this challenge will bring progress both in thetheoretical understanding of DNNs and in building new architecturesefficiently. In this work, we address this challenge by developing a newcomplexity measure based on the concept of {Periodic Spectral Ergodicity} (PSE)originating from quantum statistical mechanics. Based on this measure atechnique is devised to quantify the complexity of deep neural networks fromthe learned weights and traversing the network connectivity in a sequentialmanner, hence the term cascading PSE (cPSE), as an empirical complexitymeasure. This measure will capture both topological and internal neuralprocessing complexity simultaneously. Because of this cascading approach, i.e.,a symmetric divergence of PSE on the consecutive layers, it is possible to usethis measure for Neural Architecture Search (NAS). We demonstrate theusefulness of this measure in practice on two sets of vision models, ResNet andVGG, and sketch the computation of cPSE for more complex network structures.

Periodic Spectral Ergodicity: A Complexity Measure for Deep Neural Networks and Neural Architecture Search