{"paper":{"title":"Even More Guarantees for Variational Inference in the Presence of Symmetries","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Sufficient conditions on target symmetries guarantee exact mean recovery in variational inference with forward KL and alpha-divergences even under misspecification.","cross_cats":["stat.CO","stat.ML"],"primary_cat":"cs.LG","authors_text":"Antonio Vergari, Lena Zellinger","submitted_at":"2026-04-23T08:22:37Z","abstract_excerpt":"When approximating an intractable density via variational inference (VI) the variational family is typically chosen as a simple parametric family that very likely does not contain the target. This raises the question: Under which conditions can we recover characteristics of the target despite misspecification? In this work, we extend previous theoretical results on robust VI with location-scale families under target symmetries in two substantial ways: (1) We open them up to a wider range of divergences by providing sufficient conditions for exact recovery of the target mean and correlation mat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive sufficient conditions guaranteeing exact recovery of the mean when using the forward Kullback-Leibler divergence and α-divergences.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The target distribution possesses symmetries that interact with the location-scale variational family in a way that permits exact mean recovery under the chosen divergences.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Sufficient conditions on target symmetries guarantee exact mean recovery in variational inference with location-scale families for forward KL and alpha-divergences.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Sufficient conditions on target symmetries guarantee exact mean recovery in variational inference with forward KL and alpha-divergences even under misspecification.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f7755368ca18980e0513c5386d520bd21a11737622160bd1531345c56d22ca22"},"source":{"id":"2604.21407","kind":"arxiv","version":2},"verdict":{"id":"b8cf4777-6901-46fe-b223-9a1e36af362a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T22:21:13.357048Z","strongest_claim":"We derive sufficient conditions guaranteeing exact recovery of the mean when using the forward Kullback-Leibler divergence and α-divergences.","one_line_summary":"Sufficient conditions on target symmetries guarantee exact mean recovery in variational inference with location-scale families for forward KL and alpha-divergences.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The target distribution possesses symmetries that interact with the location-scale variational family in a way that permits exact mean recovery under the chosen divergences.","pith_extraction_headline":"Sufficient conditions on target symmetries guarantee exact mean recovery in variational inference with forward KL and alpha-divergences even under misspecification."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.21407/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T12:42:39.286561Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T00:58:26.516232Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1b80804a26c71bc31d29a0f43080c91c027cf028d32f59d657f96f6aa072df38"},"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"}