{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/natural-langevin-dynamics-for-neural-networks","title":"Natural Langevin Dynamics for Neural Networks","arxiv_id":"1712.01076","date":"2017-12-04","proceeding":null,"authors":["Gaétan Marceau-Caron","Yann Ollivier"],"abstract":"One way to avoid overfitting in machine learning is to use model parameters\ndistributed according to a Bayesian posterior given the data, rather than the\nmaximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is\none algorithm to approximate such Bayesian posteriors for large models and\ndatasets. SGLD is a standard stochastic gradient descent to which is added a\ncontrolled amount of noise, specifically scaled so that the parameter converges\nin law to the posterior distribution [WT11, TTV16]. The posterior predictive\ndistribution can be approximated by an ensemble of samples from the trajectory.\n  Choice of the variance of the noise is known to impact the practical behavior\nof SGLD: for instance, noise should be smaller for sensitive parameter\ndirections. Theoretically, it has been suggested to use the inverse Fisher\ninformation matrix of the model as the variance of the noise, since it is also\nthe variance of the Bayesian posterior [PT13, AKW12, GC11]. But the Fisher\nmatrix is costly to compute for large- dimensional models.\n  Here we use the easily computed Fisher matrix approximations for deep neural\nnetworks from [MO16, Oll15]. The resulting natural Langevin dynamics combines\nthe advantages of Amari's natural gradient descent and Fisher-preconditioned\nLangevin dynamics for large neural networks.\n  Small-scale experiments on MNIST show that Fisher matrix preconditioning\nbrings SGLD close to dropout as a regularizing technique.","url_abs":"http://arxiv.org/abs/1712.01076v1","url_pdf":"http://arxiv.org/pdf/1712.01076v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"natural-langevin-dynamics-for-neural-networks","repo_url":"https://github.com/gmarceaucaron/natural-langevin-dynamics-for-neural-networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"dropout","method_name":"Dropout"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}