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Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks

Gaël Letarte 1 Pascal Germain 2 Benjamin Guedj 3, 4, 5, 2, 6 François Laviolette 7
2 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, overcoming the fact that binary activation function is non-differentiable; (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Noteworthy, our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. The performance of our approach is assessed on a thorough numerical experiment protocol on real-life datasets.
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https://hal.inria.fr/hal-02139432
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Submitted on : Wednesday, May 29, 2019 - 2:51:29 PM
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Gaël Letarte, Pascal Germain, Benjamin Guedj, François Laviolette. Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks. NeurIPS 2019 - Thirty-third Conference on Neural Information Processing Systems, Dec 2019, Vancouver, Canada. ⟨hal-02139432v2⟩

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