{"paper":{"title":"Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT view","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Mihailo Stojnic","submitted_at":"2025-06-23T04:20:24Z","abstract_excerpt":"We analyze the relation between spectral initializers and theoretical limits of \\emph{descending} phase retrieval algorithms (dPR). In companion paper [104], for any sample complexity ratio, $\\alpha$, \\emph{parametric manifold}, ${\\mathcal {PM}}(\\alpha)$, is recognized as a critically important structure that generically determines dPRs abilities to solve phase retrieval (PR). Moreover, overlap between the algorithmic solution and the true signal is positioned as a key ${\\mathcal {PM}}$'s component. We here consider the so-called \\emph{overlap optimal} spectral initializers (OptSpins) as dPR's"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18279","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/2506.18279/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"}