{"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/infinite-width-limit-of-deep-linear-neural","title":"Infinite-width limit of deep linear neural networks","arxiv_id":"2211.16980","date":"2022-11-29","proceeding":null,"authors":["Lénaïc Chizat","Maria Colombo","Xavier Fernández-Real","Alessio Figalli"],"abstract":"This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear neural network. Moreover, even if the weights remain random, we get their precise law along the training dynamics, and prove a quantitative convergence result of the linear predictor in terms of the number of neurons. We finally study the continuous-time limit obtained for infinitely wide linear neural networks and show that the linear predictors of the neural network converge at an exponential rate to the minimal $\\ell_2$-norm minimizer of the risk.","url_abs":"https://arxiv.org/abs/2211.16980v1","url_pdf":"https://arxiv.org/pdf/2211.16980v1.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":"infinite-width-limit-of-deep-linear-neural","repo_url":"https://github.com/lchizat/2022-wide-linear-nn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2211.16980","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}