Natural Langevin Dynamics for Neural Networks

Yann Ollivier 1, 2, 3 Gaétan Marceau-Caron 4
1 TAU - TAckling the Underspecified
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGLD is a standard stochastic gradient descent to which is added a controlled amount of noise, specifically scaled so that the parameter converges in law to the posterior distribution [WT11, TTV16]. The posterior predictive distribution can be approximated by an ensemble of samples from the trajectory. Choice of the variance of the noise is known to impact the practical behavior of SGLD: for instance, noise should be smaller for sensitive parameter directions. Theoretically, it has been suggested to use the inverse Fisher information matrix of the model as the variance of the noise, since it is also the variance of the Bayesian posterior [PT13, AKW12, GC11]. But the Fisher matrix is costly to compute for large- dimensional models. Here we use the easily computed Fisher matrix approximations for deep neural networks from [MO16, Oll15]. The resulting natural Langevin dynamics combines the advantages of Amari's natural gradient descent and Fisher-preconditioned Langevin dynamics for large neural networks. Small-scale experiments on MNIST show that Fisher matrix preconditioning brings SGLD close to dropout as a regularizing technique.
Type de document :
Communication dans un congrès
GSI 2017 - 3rd conference on Geometric Science of Information, Nov 2017, Paris, France. Springer Verlag, LNCS, 10589, pp.451-459, 〈https://www.see.asso.fr/gsi2017〉. 〈10.1007/978-3-319-68445-1_53〉
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Contributeur : Yann Ollivier <>
Soumis le : mardi 5 décembre 2017 - 12:12:49
Dernière modification le : mardi 8 janvier 2019 - 08:36:01

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Yann Ollivier, Gaétan Marceau-Caron. Natural Langevin Dynamics for Neural Networks. GSI 2017 - 3rd conference on Geometric Science of Information, Nov 2017, Paris, France. Springer Verlag, LNCS, 10589, pp.451-459, 〈https://www.see.asso.fr/gsi2017〉. 〈10.1007/978-3-319-68445-1_53〉. 〈hal-01655949〉

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