Harmonic Decompositions of Convolutional Networks

Jul 12, 2020

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We present a description of function spaces and smoothness classes associated with convolutional networks from a reproducing kernel Hilbert space viewpoint. We establish harmonic decompositions of convolutional networks, that is expansions into sums of elementary functions of feature-representation maps implemented by convolutional networks. The elementary functions are related to the spherical harmonics, a fundamental class of special functions on spheres. These harmonic decompositions allow us to characterize the integral operators associated with convolutional networks, and obtain as a result risk bounds for convolutional networks which highlight their behavior in high dimensions.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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