{"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/scaling-resnets-in-the-large-depth-regime","title":"Scaling ResNets in the Large-depth Regime","arxiv_id":"2206.06929","date":"2022-06-14","proceeding":null,"authors":["Pierre Marion","Adeline Fermanian","Gérard Biau","Jean-Philippe Vert"],"abstract":"Deep ResNets are recognized for achieving state-of-the-art results in complex machine learning tasks. However, the remarkable performance of these architectures relies on a training procedure that needs to be carefully crafted to avoid vanishing or exploding gradients, particularly as the depth $L$ increases. No consensus has been reached on how to mitigate this issue, although a widely discussed strategy consists in scaling the output of each layer by a factor $\\alpha_L$. We show in a probabilistic setting that with standard i.i.d.~initializations, the only non-trivial dynamics is for $\\alpha_L = \\frac{1}{\\sqrt{L}}$; other choices lead either to explosion or to identity mapping. This scaling factor corresponds in the continuous-time limit to a neural stochastic differential equation, contrarily to a widespread interpretation that deep ResNets are discretizations of neural ordinary differential equations. By contrast, in the latter regime, stability is obtained with specific correlated initializations and $\\alpha_L = \\frac{1}{L}$. Our analysis suggests a strong interplay between scaling and regularity of the weights as a function of the layer index. Finally, in a series of experiments, we exhibit a continuous range of regimes driven by these two parameters, which jointly impact performance before and after training.","url_abs":"https://arxiv.org/abs/2206.06929v2","url_pdf":"https://arxiv.org/pdf/2206.06929v2.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":"scaling-resnets-in-the-large-depth-regime","repo_url":"https://github.com/pierremarion23/scaling-resnets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2206.06929","atlas_url":"https://app.syntology.ai/?focus=2206.06929","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.06929"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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