{"paper":{"title":"Optimization of Mean-field Spin Glasses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.OC"],"primary_cat":"math.PR","authors_text":"Ahmed El Alaoui, Andrea Montanari, Mark Sellke","submitted_at":"2020-01-03T17:39:35Z","abstract_excerpt":"Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper we consider the case of Ising mixed $p$-spin models, namely Hamiltonians $H_N:\\Sigma_N\\to {\\mathbb R}$ on the Hamming hypercube $\\Sigma_N = \\{\\pm 1\\}^N$, which are defined by the property that $\\{H_N({\\boldsymbol \\sigma})\\}_{{\\boldsymbol \\sigma}\\in \\Sigma_N}$ is a centered Gaussian process with covariance ${\\mathbb E}\\{H_N({\\boldsymbol \\sigma}_1)H_N({\\boldsymbol \\sigma}_2)\\}$ depending only on the scalar product $\\langle {\\boldsymbol \\sigma}_1,{\\boldsymbol \\sigma}_2\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.00904","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/2001.00904/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"}