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pith:FK2RKBBY

pith:2026:FK2RKBBYVZUMSB2MVEK3FOUR3U

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Controlling Transient Amplification Improves Long-horizon Rollouts

Adeel Pervez, Francesco Locatello

Non-normal and non-commuting Jacobians along rollout trajectories cause transient error amplification and long-horizon drift even in asymptotically stable systems.

arxiv:2605.08856 v2 · 2026-05-09 · cs.LG

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

21 extracted · 21 resolved · 2 Pith anchors

[1] 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 1999

[2] URLhttps://rmets.onlinelibrary · doi:10.1002/qj.3803

[3] 15 Controlling Transient Amplification Improves Long-horizon Rollouts doi: https://doi.org/10.1016/j.neunet.2026.108641 2026 · doi:10.1016/j.neunet.2026.108641

[4] 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. St · doi:10.1007/bf01957346

[5] Learning skillful medium-range global weather forecasting · doi:10.1126/science.adi2336

Receipt and verification

First computed	2026-05-20T00:00:41.641197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ab5150438ae68c9074ca915b2ba91dd26c065ff66e680984aaeb6ed86732833

Aliases

arxiv: 2605.08856 · arxiv_version: 2605.08856v2 · doi: 10.48550/arxiv.2605.08856 · pith_short_12: FK2RKBBYVZUM · pith_short_16: FK2RKBBYVZUMSB2M · pith_short_8: FK2RKBBY

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/FK2RKBBYVZUMSB2MVEK3FOUR3U \
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# expect: 2ab5150438ae68c9074ca915b2ba91dd26c065ff66e680984aaeb6ed86732833

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-09T10:10:30Z",
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