{"paper":{"title":"Spectral Ergodicity in Deep Learning Architectures via Surrogate Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG"],"primary_cat":"stat.ML","authors_text":"Cornelius Weber, Joan J. Cerd\\`a, Mehmet S\\\"uzen","submitted_at":"2017-04-25T17:26:08Z","abstract_excerpt":"In this work a novel method to quantify spectral ergodicity for random matrices is presented. The new methodology combines approaches rooted in the metrics of Thirumalai-Mountain (TM) and Kullbach-Leibler (KL) divergence. The method is applied to a general study of deep and recurrent neural networks via the analysis of random matrix ensembles mimicking typical weight matrices of those systems. In particular, we examine circular random matrix ensembles: circular unitary ensemble (CUE), circular orthogonal ensemble (COE), and circular symplectic ensemble (CSE). Eigenvalue spectra and spectral er"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08303","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}