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Conference papers
Understanding Priors in Bayesian Neural Networks at the Unit Level
Abstract : We investigate deep Bayesian neural networks with Gaussian priors on the weights and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, “weight decay”, regularization. Our results indicate a more intricate regularization effect at the level of the unit activations. Our main result establishes that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. We show that first layer units are Gaussian, second layer units are sub-exponential, and units in deeper layers are characterized by sub-Weibull distributions. Our results provide new theoretical insight on deep Bayesian neural networks, which we corroborate with simulation experiments.
Cited literature [14 references]
https://hal.archives-ouvertes.fr/hal-02177151
Contributor : Mariia Vladimirova <>
Submitted on : Monday, July 8, 2019 - 4:27:43 PM
Last modification on : Tuesday, May 11, 2021 - 11:37:39 AM
Contributor : Mariia Vladimirova <>
Submitted on : Monday, July 8, 2019 - 4:27:43 PM
Last modification on : Tuesday, May 11, 2021 - 11:37:39 AM
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paper_arXiv_ICML2019-3.pdf
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