{"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/wide-stochastic-networks-gaussian-limit-and","title":"Wide stochastic networks: Gaussian limit and PAC-Bayesian training","arxiv_id":"2106.09798","date":"2021-06-17","proceeding":null,"authors":["Eugenio Clerico","George Deligiannidis","Arnaud Doucet"],"abstract":"The limit of infinite width allows for substantial simplifications in the analytical study of over-parameterised neural networks. With a suitable random initialisation, an extremely large network exhibits an approximately Gaussian behaviour. In the present work, we establish a similar result for a simple stochastic architecture whose parameters are random variables, holding both before and during training. The explicit evaluation of the output distribution allows for a PAC-Bayesian training procedure that directly optimises the generalisation bound. For a large but finite-width network, we show empirically on MNIST that this training approach can outperform standard PAC-Bayesian methods.","url_abs":"https://arxiv.org/abs/2106.09798v3","url_pdf":"https://arxiv.org/pdf/2106.09798v3.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":"wide-stochastic-networks-gaussian-limit-and","repo_url":"https://github.com/eclerico/WideStochNet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2106.09798","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}