{"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/on-the-training-dynamics-of-deep-networks","title":"On the training dynamics of deep networks with $L_2$ regularization","arxiv_id":"2006.08643","date":"2020-06-15","proceeding":"NeurIPS 2020 12","authors":["Aitor Lewkowycz","Guy Gur-Ari"],"abstract":"We study the role of $L_2$ regularization in deep learning, and uncover simple relations between the performance of the model, the $L_2$ coefficient, the learning rate, and the number of training steps. These empirical relations hold when the network is overparameterized. They can be used to predict the optimal regularization parameter of a given model. In addition, based on these observations we propose a dynamical schedule for the regularization parameter that improves performance and speeds up training. We test these proposals in modern image classification settings. Finally, we show that these empirical relations can be understood theoretically in the context of infinitely wide networks. We derive the gradient flow dynamics of such networks, and compare the role of $L_2$ regularization in this context with that of linear models.","url_abs":"https://arxiv.org/abs/2006.08643v2","url_pdf":"https://arxiv.org/pdf/2006.08643v2.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":"on-the-training-dynamics-of-deep-networks","repo_url":"https://github.com/google/autol2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2006.08643","atlas_url":"https://app.syntology.ai/?focus=2006.08643","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2006.08643"}},"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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