{"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/explicit-regularization-in-overparametrized","title":"Explicit Regularization in Overparametrized Models via Noise Injection","arxiv_id":"2206.04613","date":"2022-06-09","proceeding":null,"authors":["Antonio Orvieto","Anant Raj","Hans Kersting","Francis Bach"],"abstract":"Injecting noise within gradient descent has several desirable features, such as smoothing and regularizing properties. In this paper, we investigate the effects of injecting noise before computing a gradient step. We demonstrate that small perturbations can induce explicit regularization for simple models based on the L1-norm, group L1-norms, or nuclear norms. However, when applied to overparametrized neural networks with large widths, we show that the same perturbations can cause variance explosion. To overcome this, we propose using independent layer-wise perturbations, which provably allow for explicit regularization without variance explosion. Our empirical results show that these small perturbations lead to improved generalization performance compared to vanilla gradient descent.","url_abs":"https://arxiv.org/abs/2206.04613v3","url_pdf":"https://arxiv.org/pdf/2206.04613v3.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":"explicit-regularization-in-overparametrized","repo_url":"https://github.com/aorvieto/noise_injection_overparam","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.04613","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}