{"paper":{"title":"Continuized Nesterov Momentum Achieves the $O(\\varepsilon^{-7/4})$ Complexity without Additional Mechanisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aude Rondepierre, Charles Dossal, Ir\\`ene Waldspurger, Jean-Fran\\c{c}ois Aujol, Julien Hermant, Lorick Huang","submitted_at":"2026-02-05T10:05:47Z","abstract_excerpt":"For first-order optimization of non-convex functions with Lipschitz continuous gradient and Hessian, the best known complexity for reaching an $\\varepsilon$-approximation of a stationary point is $O(\\varepsilon^{-7/4})$. Existing algorithms achieving this bound are based on momentum, but are always complemented with safeguard mechanisms, such as restarts or negative-curvature exploitation steps. Whether such mechanisms are fundamentally necessary has remained an open question. Leveraging the continuized method, we show that a Nesterov momentum algorithm with stochastic parameters alone achieve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.05504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.05504/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"}