{"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/train-deep-neural-networks-in-40-d-subspaces","title":"Low Dimensional Landscape Hypothesis is True: DNNs can be Trained in Tiny Subspaces","arxiv_id":"2103.11154","date":"2021-03-20","proceeding":null,"authors":["Tao Li","Lei Tan","Qinghua Tao","Yipeng Liu","Xiaolin Huang"],"abstract":"Deep neural networks (DNNs) usually contain massive parameters, but there is redundancy such that it is guessed that the DNNs could be trained in low-dimensional subspaces. In this paper, we propose a Dynamic Linear Dimensionality Reduction (DLDR) based on low-dimensional properties of the training trajectory. The reduction is efficient, which is supported by comprehensive experiments: optimization in 40 dimensional spaces can achieve comparable performance as regular training over thousands or even millions of parameters. Since there are only a few optimization variables, we develop a quasi-Newton-based algorithm and also obtain robustness against label noises, which are two follow-up experiments to show the advantages of finding low-dimensional subspaces.","url_abs":"https://arxiv.org/abs/2103.11154v2","url_pdf":"https://arxiv.org/pdf/2103.11154v2.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":"train-deep-neural-networks-in-40-d-subspaces","repo_url":"https://github.com/nblt/DLDR","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2103.11154","atlas_url":"https://app.syntology.ai/?focus=2103.11154","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}