{"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/analysis-of-gradient-clipping-and-adaptive","title":"Why gradient clipping accelerates training: A theoretical justification for adaptivity","arxiv_id":"1905.11881","date":"2019-05-28","proceeding":"ICLR 2020 1","authors":["Jingzhao Zhang","Tianxing He","Suvrit Sra","Ali Jadbabaie"],"abstract":"We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks. The key ingredient is a new smoothness condition derived from practical neural network training examples. We observe that gradient smoothness, a concept central to the analysis of first-order optimization algorithms that is often assumed to be a constant, demonstrates significant variability along the training trajectory of deep neural networks. Further, this smoothness positively correlates with the gradient norm, and contrary to standard assumptions in the literature, it can grow with the norm of the gradient. These empirical observations limit the applicability of existing theoretical analyses of algorithms that rely on a fixed bound on smoothness. These observations motivate us to introduce a novel relaxation of gradient smoothness that is weaker than the commonly used Lipschitz smoothness assumption. Under the new condition, we prove that two popular methods, namely, \\emph{gradient clipping} and \\emph{normalized gradient}, converge arbitrarily faster than gradient descent with fixed stepsize. We further explain why such adaptively scaled gradient methods can accelerate empirical convergence and verify our results empirically in popular neural network training settings.","url_abs":"https://arxiv.org/abs/1905.11881v2","url_pdf":"https://arxiv.org/pdf/1905.11881v2.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":"analysis-of-gradient-clipping-and-adaptive","repo_url":"https://github.com/JingzhaoZhang/why-clipping-accelerates","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"language-modelling","task_name":"Language Modelling"}],"methods":[{"method_slug":"gradient-clipping","method_name":"Gradient Clipping"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.11881","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.11881"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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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