{"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/from-high-dimensional-mean-field-dynamics-to","title":"From high-dimensional & mean-field dynamics to dimensionless ODEs: A unifying approach to SGD in two-layers networks","arxiv_id":"2302.05882","date":"2023-02-12","proceeding":null,"authors":["Luca Arnaboldi","Ludovic Stephan","Florent Krzakala","Bruno Loureiro"],"abstract":"This manuscript investigates the one-pass stochastic gradient descent (SGD) dynamics of a two-layer neural network trained on Gaussian data and labels generated by a similar, though not necessarily identical, target function. We rigorously analyse the limiting dynamics via a deterministic and low-dimensional description in terms of the sufficient statistics for the population risk. Our unifying analysis bridges different regimes of interest, such as the classical gradient-flow regime of vanishing learning rate, the high-dimensional regime of large input dimension, and the overparameterised \"mean-field\" regime of large network width, covering as well the intermediate regimes where the limiting dynamics is determined by the interplay between these behaviours. In particular, in the high-dimensional limit, the infinite-width dynamics is found to remain close to a low-dimensional subspace spanned by the target principal directions. Our results therefore provide a unifying picture of the limiting SGD dynamics with synthetic data.","url_abs":"https://arxiv.org/abs/2302.05882v1","url_pdf":"https://arxiv.org/pdf/2302.05882v1.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":"from-high-dimensional-mean-field-dynamics-to","repo_url":"https://github.com/idephics/dimensionlessdynamicssgd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2302.05882","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}