{"paper":{"title":"Anytime and Difficulty-Adaptive PAC-Bayes for Constrained Density-Ratio Network with Continual Learning Guarantees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Paulo Akira F. Enabe","submitted_at":"2026-05-17T01:07:17Z","abstract_excerpt":"A unified framework for learning under covariate shift is presented, in which a constrained density-ratio network approximates the Radon-Nikodym derivative $r^\\star = dP/dQ$ from source $Q$ to target $P$, supports an importance-weighted empirical risk, and feeds an anytime PAC-Bayes generalization certificate. A change-of-measure identity decomposes the gap between target risk and importance-weighted source risk into a ratio-bias term, controlled by the $L^2(Q)$ closeness of the learned ratio to $r^\\star$, and a generalization-gap term, controlled by the variability of the weighted loss. Three"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17212","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/2605.17212/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.724588Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.929143Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7e4908a8691ba6315326e34f75db2be5bab7c28b1f15906043e8739ab1f604da"},"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"}