{"paper":{"title":"Spectral Smoothing via Random Matrix Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ambuj Tewari, Chansoo Lee, Jacob Abernethy","submitted_at":"2015-07-10T20:52:35Z","abstract_excerpt":"We consider stochastic smoothing of spectral functions of matrices using perturbations commonly studied in random matrix theory. We show that a spectral function remains spectral when smoothed using a unitarily invariant perturbation distribution. We then derive state-of-the-art smoothing bounds for the maximum eigenvalue function using the Gaussian Orthogonal Ensemble (GOE). Smoothing the maximum eigenvalue function is important for applications in semidefinite optimization and online learning. As a direct consequence of our GOE smoothing results, we obtain an $O((N \\log N)^{1/4} \\sqrt{T})$ e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03032","kind":"arxiv","version":2},"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"}