{"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/fisher-rao-metric-geometry-and-complexity-of","title":"Fisher-Rao Metric, Geometry, and Complexity of Neural Networks","arxiv_id":"1711.01530","date":"2017-11-05","proceeding":null,"authors":["Tengyuan Liang","Tomaso Poggio","Alexander Rakhlin","James Stokes"],"abstract":"We study the relationship between geometry and capacity measures for deep\nneural networks from an invariance viewpoint. We introduce a new notion of\ncapacity --- the Fisher-Rao norm --- that possesses desirable invariance\nproperties and is motivated by Information Geometry. We discover an analytical\ncharacterization of the new capacity measure, through which we establish\nnorm-comparison inequalities and further show that the new measure serves as an\numbrella for several existing norm-based complexity measures. We discuss upper\nbounds on the generalization error induced by the proposed measure. Extensive\nnumerical experiments on CIFAR-10 support our theoretical findings. Our\ntheoretical analysis rests on a key structural lemma about partial derivatives\nof multi-layer rectifier networks.","url_abs":"http://arxiv.org/abs/1711.01530v2","url_pdf":"http://arxiv.org/pdf/1711.01530v2.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":"fisher-rao-metric-geometry-and-complexity-of","repo_url":"https://github.com/ML-KA/PDG-Theory","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"lemma","task_name":"LEMMA"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1711.01530","atlas_url":"https://app.syntology.ai/?focus=1711.01530","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}