{"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/spectral-ergodicity-in-deep-learning","title":"Spectral Ergodicity in Deep Learning Architectures via Surrogate Random Matrices","arxiv_id":"1704.08303","date":"2017-04-25","proceeding":null,"authors":["Mehmet Süzen","Cornelius Weber","Joan J. Cerdà"],"abstract":"In this work a novel method to quantify spectral ergodicity for random\nmatrices is presented. The new methodology combines approaches rooted in the\nmetrics of Thirumalai-Mountain (TM) and Kullbach-Leibler (KL) divergence. The\nmethod is applied to a general study of deep and recurrent neural networks via\nthe analysis of random matrix ensembles mimicking typical weight matrices of\nthose systems. In particular, we examine circular random matrix ensembles:\ncircular unitary ensemble (CUE), circular orthogonal ensemble (COE), and\ncircular symplectic ensemble (CSE). Eigenvalue spectra and spectral ergodicity\nare computed for those ensembles as a function of network size. It is observed\nthat as the matrix size increases the level of spectral ergodicity of the\nensemble rises, i.e., the eigenvalue spectra obtained for a single realisation\nat random from the ensemble is closer to the spectra obtained averaging over\nthe whole ensemble. Based on previous results we conjecture that success of\ndeep learning architectures is strongly bound to the concept of spectral\nergodicity. The method to compute spectral ergodicity proposed in this work\ncould be used to optimise the size and architecture of deep as well as\nrecurrent neural networks.","url_abs":"http://arxiv.org/abs/1704.08303v3","url_pdf":"http://arxiv.org/pdf/1704.08303v3.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":"spectral-ergodicity-in-deep-learning","repo_url":"https://github.com/msuzen/bristol","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}