{"paper":{"title":"The Riemannian barycentre as a proxy for global optimisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jonathan H. Manton, Salem Said","submitted_at":"2019-02-11T14:07:36Z","abstract_excerpt":"Let $M$ be a simply-connected compact Riemannian symmetric space, and $U$ a twice-differentiable function on $M$, with unique global minimum at $x^* \\in M$. The idea of the present work is to replace the problem of searching for the global minimum of $U$, by the problem of finding the Riemannian barycentre of the Gibbs distribution $P_{\\scriptscriptstyle{T}} \\propto \\exp(-U/T)$. In other words, instead of minimising the function $U$ itself, to minimise $\\mathcal{E}_{\\scriptscriptstyle{T}}(x) = \\frac{1}{2}\\int d^{\\scriptscriptstyle 2}(x,z)P_{\\scriptscriptstyle{T}}(dz)$, where $d(\\cdot,\\cdot)$ d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03885","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":""},"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"}