{"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/a-coding-theoretic-analysis-of-hyperspherical","title":"A Coding-Theoretic Analysis of Hyperspherical Prototypical Learning Geometry","arxiv_id":"2407.07664","date":"2024-07-10","proceeding":null,"authors":["Martin Lindström","Borja Rodríguez-Gálvez","Ragnar Thobaben","Mikael Skoglund"],"abstract":"Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known geometry. Previous approaches to HPL have either of the following shortcomings: (i) they follow an unprincipled optimisation procedure; or (ii) they are theoretically sound, but are constrained to only one possible latent dimension. In this paper, we address both shortcomings. To address (i), we present a principled optimisation procedure whose solution we show is optimal. To address (ii), we construct well-separated prototypes in a wide range of dimensions using linear block codes. Additionally, we give a full characterisation of the optimal prototype placement in terms of achievable and converse bounds, showing that our proposed methods are near-optimal.","url_abs":"https://arxiv.org/abs/2407.07664v2","url_pdf":"https://arxiv.org/pdf/2407.07664v2.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":"a-coding-theoretic-analysis-of-hyperspherical","repo_url":"https://github.com/martinlindstrom/coding_theoretic_hpl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}