{"paper":{"title":"Controlling Transient Amplification Improves Long-horizon Rollouts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Non-normal and non-commuting Jacobians along rollout trajectories cause transient error amplification and long-horizon drift even in asymptotically stable systems.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Adeel Pervez, Francesco Locatello","submitted_at":"2026-05-09T10:10:30Z","abstract_excerpt":"Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on th"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"When Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in rollout drift even when the overall system is asymptotically stable; commutativity regularization reduces this amplification and enables successful long-horizon rollouts over thousands of steps.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The linearization analysis around rollout trajectories captures the dominant source of long-horizon error, and the two proposed penalties can be tuned to reduce normality defect and commutator norm without introducing new instabilities or degrading short-horizon accuracy.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-normal and non-commuting Jacobians along rollout trajectories cause transient error amplification and long-horizon drift even in asymptotically stable systems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"15393305ba45e6f2631f8b1d1c74647f45c44093ae117fc75608d75b15049aac"},"source":{"id":"2605.08856","kind":"arxiv","version":2},"verdict":{"id":"31b79906-79d3-46f3-865d-5b6666e992be","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:39:39.855830Z","strongest_claim":"When Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in rollout drift even when the overall system is asymptotically stable; commutativity regularization reduces this amplification and enables successful long-horizon rollouts over thousands of steps.","one_line_summary":"Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The linearization analysis around rollout trajectories captures the dominant source of long-horizon error, and the two proposed penalties can be tuned to reduce normality defect and commutator norm without introducing new instabilities or degrading short-horizon accuracy.","pith_extraction_headline":"Non-normal and non-commuting Jacobians along rollout trajectories cause transient error amplification and long-horizon drift even in asymptotically stable systems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.08856/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:44.975825Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T14:01:21.685923Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:42:26.659571Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"62e724dfd9d71b526be8f3ae2d60fb0d9691bf74262f34d8447e717e47833f94"},"references":{"count":21,"sample":[{"doi":"","year":1999,"title":"URLhttps://openreview.net/forum?id=MKP1g8wU0P. H. Hersbach, B. Bell, P. Berrisford, S. Hirahara, A. Horányi, J. Muñoz-Sabater, J. Nicolas, C. Peubey, R. Radu, D. Schepers, A. Simmons, C. Soci, S. Abda","work_id":"84276261-9515-4224-b79a-231761f749d7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1002/qj.3803","year":null,"title":"URLhttps://rmets.onlinelibrary","work_id":"e8d7a404-9f91-4f76-95f8-6949c6500cfa","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.neunet.2026.108641","year":2026,"title":"15 Controlling Transient Amplification Improves Long-horizon Rollouts doi: https://doi.org/10.1016/j.neunet.2026.108641","work_id":"21318679-1824-4bf5-8e62-8abbb66d018f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/bf01957346","year":null,"title":"doi: 10.1007/BF01957346. R. Lam, A. Sanchez-Gonzalez, M. Willson, P. Wirnsberger, M. Fortunato, F. Alet, S. Ravuri, T. Ewalds, Z. Eaton-Rosen, W. Hu, A. Merose, S. Hoyer, G. Holland, O. Vinyals, J. 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