{"paper":{"title":"Generative models for decision-making under distributional shift","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Generative models construct nominal, stressed, and conditional distributions for decisions under shift using transport maps and guided dynamics.","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Xiuyuan Cheng, Yao Xie, Yunqin Zhu","submitted_at":"2026-04-06T01:35:13Z","abstract_excerpt":"Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced. This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions. From an operations research perspective, their primary value lies not in unconstrained sample synthesis but in representing and transforming distributions through transport "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation, within a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the mathematical tools (transport maps, score fields, guided stochastic dynamics) can be trained and deployed in a way that reliably produces decision-relevant distributions whose properties transfer to the actual deployment distribution under shift.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generative models via pushforward maps, Fokker-Planck equations, and Wasserstein geometry enable learning nominal uncertainty, stressed distributions for robustness, and conditional posteriors under distributional shift.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Generative models construct nominal, stressed, and conditional distributions for decisions under shift using transport maps and guided dynamics.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6a8532b084197954d4520c582d2128644a04dd013b87f55c19a338c26b5ef8a6"},"source":{"id":"2604.04342","kind":"arxiv","version":2},"verdict":{"id":"6592cbfb-ce6e-4c96-bf8a-cf3a32741ab0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T20:24:13.117908Z","strongest_claim":"Generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation, within a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space.","one_line_summary":"Generative models via pushforward maps, Fokker-Planck equations, and Wasserstein geometry enable learning nominal uncertainty, stressed distributions for robustness, and conditional posteriors under distributional shift.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the mathematical tools (transport maps, score fields, guided stochastic dynamics) can be trained and deployed in a way that reliably produces decision-relevant distributions whose properties transfer to the actual deployment distribution under shift.","pith_extraction_headline":"Generative models construct nominal, stressed, and conditional distributions for decisions under shift using transport maps and guided dynamics."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.04342/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":2,"snapshot_sha256":"6f36de3cc61172c565129c2cd6493e14f08b376e87cb1293db1cc55dce4e6494"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}