{"paper":{"title":"Smooth globally PLI functions are nonlinear least-squares, and so are their gradient-dominated cousins","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","math.DG","math.DS"],"primary_cat":"eess.SY","authors_text":"Eduardo D. Sontag","submitted_at":"2026-08-09T18:24:48Z","abstract_excerpt":"Boumal, Criscitiello and Rebjock (BCR) in [arXiv:2604.07972, 2026] proved that a smooth real-valued function f defined on a contractible complete Riemannian manifold which satisfies the (global) Polyak-Lojasiewicz inequality (PLI) is necessarily of the form f = f* + phi^2, with phi a submersion, together with a long list of consequences. That hypothesis is unfortunately not available in several problems where one most wants it, among them continuous-time LQR policy optimization and logistic regression, and this is what motivated the hierarchy of generalized PLI inequalities developed several p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08849","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08849/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}