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arXiv · 1802.09979

The Emergence of Spectral Universality in Deep Networks

Jeffrey Pennington·Samuel S. Schoenholz·Surya Ganguli
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Abstract

Recent work has shown that tight concentration of the entire spectrum of singular values of a deep network's input-output Jacobian around one at initialization can speed up learning by orders of magnitude. Therefore, to guide important design choices, it is important to build a full theoretical understanding of the spectra of Jacobians at initialization. To this end, we leverage powerful tools from free probability theory to provide a detailed analytic understanding of how a deep network's Jacobian spectrum depends on various hyperparameters including the nonlinearity, the weight and bias distributions, and the depth. For a variety of nonlinearities, our work reveals the emergence of new universal limiting spectral distributions that remain concentrated around one even as the depth goes to infinity.

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Jeffrey Pennington, Samuel S. Schoenholz, Surya Ganguli. 2018-02-27. The Emergence of Spectral Universality in Deep Networks. https://arxiv.org/abs/1802.09979

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