{"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/simplicial-regularization","title":"Simplicial Regularization","arxiv_id":null,"date":"2021-03-08","proceeding":"ICLR Workshop GTRL 2021 5","authors":["Jose Gallego-Posada","Patrick Forré"],"abstract":"Inspired by the fuzzy topological representation of a dataset employed in UMAP (McInnes et al., 2018), we propose a regularization principle for supervised learning based on the preservation of the simplicial complex structure of the data. We analyze the behavior of our proposal in contrast with the mixup (Zhang et al., 2018) framework on dimensionality reduction and classification tasks. Our experiments show how simplicial regularization induces more appropriate learning biases and alleviates some of the shortcomings of state-of-the art methods for regularization based on data augmentation.","url_abs":"https://openreview.net/forum?id=x9xn6HKgefz","url_pdf":"https://openreview.net/pdf?id=x9xn6HKgefz","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":"simplicial-regularization","repo_url":"https://github.com/jgalle29/simplicial_regularization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"data-augmentation","task_name":"Data Augmentation"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[{"method_slug":"mixup","method_name":"Mixup"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}