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Prediction Limits and Koopman Closure of Geometry-Induced Soft State Abstractions — arXiv:2609.32652

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.32652
License (as archived): CC0-1.0
Archived: 2026-10-07T20:55:51.226Z
SHA-256 of the archived text: e4cfa110e891789e9d737803d0ef92edfe0ba0ac74f8d856d83ecdd46e569d37
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How to cite

Prediction Limits and Koopman Closure of Geometry-Induced Soft State Abstractions — arXiv:2609.32652 — arXiv (en), https://arxiv.org/abs/2609.32652 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_50f9c1237a84 (Metraipolis archive dc_50f9c1237a84, sha256 e4cfa110e891789e9d737803d0ef92edfe0ba0ac74f8d856d83ecdd46e569d37)

BibTeX

@misc{dc50f9c1237a84,
  title = {Prediction Limits and Koopman Closure of Geometry-Induced Soft State Abstractions — arXiv:2609.32652},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.32652},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_50f9c1237a84; sha256 e4cfa110e891789e9d737803d0ef92edfe0ba0ac74f8d856d83ecdd46e569d37},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.32652. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A soft state representation assigns each state a vector of nonnegative class weights that sum to one. We study how the construction of these weights and the state dynamics jointly determine the accuracy of linear prediction. For any fixed measurable representation, we derive a finite-sample lower confidence bound on the smallest population root-mean-square prediction error among matrices with a specified spectral-norm limit. The bound compares variation in successor coordinates within each reference class with the improvement that soft inputs could provide. It is computed from independent evaluation pairs without fitting a prediction matrix. A bound above a chosen tolerance rules out that tolerance for the entire matrix class; a zero bound is inconclusive. For coordinates constructed using Kernel Affine Hull Machines, reconstruction-score margins control disagreement with reference labels and enter bounds on prediction error. Under exact deterministic linear evolution, we also establish the Koopman and reproducing-kernel Hilbert-space adjoint interpretation, accounting for redundant coefficient vectors. A four-state study compares the confidence bound with analytically known optima across 117,000 reported replicate datasets. A Van der Pol representation selected on pilot data is then evaluated on 32 independent datasets under each of two transition laws. The reported bounds are positive at the fitted matrix norm, but can become zero at larger norm limits. Further forecasting studies examine coordinate variation, common prediction targets, and long-horizon error. The results distinguish agreement with reconstruction classes, attainable prediction accuracy, and exact operator closure.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-29 in cs.AI).
Categorie arXiv: Artificial Intelligence (cs.AI) ; Machine Learning (cs.LG); Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2609.32652 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T20:29:00.902Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).