{"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/the-emergence-of-spectral-universality-in","title":"The Emergence of Spectral Universality in Deep Networks","arxiv_id":"1802.09979","date":"2018-02-27","proceeding":null,"authors":["Jeffrey Pennington","Samuel S. Schoenholz","Surya Ganguli"],"abstract":"Recent work has shown that tight concentration of the entire spectrum of\nsingular values of a deep network's input-output Jacobian around one at\ninitialization can speed up learning by orders of magnitude. Therefore, to\nguide important design choices, it is important to build a full theoretical\nunderstanding of the spectra of Jacobians at initialization. To this end, we\nleverage powerful tools from free probability theory to provide a detailed\nanalytic understanding of how a deep network's Jacobian spectrum depends on\nvarious hyperparameters including the nonlinearity, the weight and bias\ndistributions, and the depth. For a variety of nonlinearities, our work reveals\nthe emergence of new universal limiting spectral distributions that remain\nconcentrated around one even as the depth goes to infinity.","url_abs":"http://arxiv.org/abs/1802.09979v1","url_pdf":"http://arxiv.org/pdf/1802.09979v1.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":"the-emergence-of-spectral-universality-in","repo_url":"https://github.com/mebassett/ncg-convnet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1802.09979","atlas_url":"https://app.syntology.ai/?focus=1802.09979","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}