{"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/estimating-the-local-learning-coefficient-at","title":"Estimating the Local Learning Coefficient at Scale","arxiv_id":"2402.03698","date":"2024-02-06","proceeding":null,"authors":["Zach Furman","Edmund Lau"],"abstract":"The \\textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically estimating the local learning coefficient, but so far these methods have not been extended to the scale of modern deep learning architectures or data sets. Using a method developed in {\\tt arXiv:2308.12108 [stat.ML]} we empirically show how the LLC may be measured accurately and self-consistently for deep linear networks (DLNs) up to 100M parameters. We also show that the estimated LLC has the rescaling invariance that holds for the theoretical quantity.","url_abs":"https://arxiv.org/abs/2402.03698v2","url_pdf":"https://arxiv.org/pdf/2402.03698v2.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":"estimating-the-local-learning-coefficient-at","repo_url":"https://github.com/cxtraa/ngd_with_slt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"learning-theory","task_name":"Learning Theory"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.03698","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}