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However, the reasons behind its merits remained unanswered, with\nseveral shortcomings that hindered its use for certain tasks. In this work, we\npresent a novel view on the purpose and function of normalization methods and\nweight-decay, as tools to decouple weights' norm from the underlying optimized\nobjective. This property highlights the connection between practices such as\nnormalization, weight decay and learning-rate adjustments. We suggest several\nalternatives to the widely used $L^2$ batch-norm, using normalization in $L^1$\nand $L^\\infty$ spaces that can substantially improve numerical stability in\nlow-precision implementations as well as provide computational and memory\nbenefits. We demonstrate that such methods enable the first batch-norm\nalternative to work for half-precision implementations. Finally, we suggest a\nmodification to weight-normalization, which improves its performance on\nlarge-scale tasks.","url_abs":"http://arxiv.org/abs/1803.01814v3","url_pdf":"http://arxiv.org/pdf/1803.01814v3.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":"norm-matters-efficient-and-accurate","repo_url":"https://github.com/eladhoffer/norm_matters","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"norm-matters-efficient-and-accurate","repo_url":"https://github.com/Abhimanyu08/L-1_BatchNorm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"norm-matters-efficient-and-accurate","repo_url":"https://github.com/eladhoffer/convNet.pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"norm-matters-efficient-and-accurate","repo_url":"https://github.com/vaapopescu/gradient-pruning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"weight-decay","method_name":"Weight Decay"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1803.01814","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1803.01814"}},"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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