{"paper":{"title":"Deriving Approximate Message Passing from the Convex Gaussian Min-Max Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Babak Hassibi, Vikrant Malik","submitted_at":"2026-06-26T06:54:53Z","abstract_excerpt":"Approximate message passing (AMP) provides fast iterative algorithms for high-dimensional signal recovery with Gaussian design matrices, while the Convex Gaussian Min-max Theorem (CGMT) gives a static optimization framework for obtaining sharp asymptotic characterizations of convex estimators. Although these two frameworks often lead to the same scalar state-evolution equations, their connection is usually indirect. In this paper, we establish a direct connection between the two for regularized linear regression in the proportional high-dimensional regime. When the CGMT Auxiliary Optimization "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27769","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/2606.27769/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"}