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Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control — arXiv:2608.07265

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.07265
License (as archived): CC0-1.0
Archived: 2026-10-18T06:36:28.686Z
SHA-256 of the archived text: f24e751cb2fa323e5a71dfc94e35bb2080102ca7f24ac7d070acaebd14524a42
Stable URL of this page: https://metraipolis.com/documento/dc_dbca0ce4dc89

How to cite

Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control — arXiv:2608.07265 — arXiv (en), https://arxiv.org/abs/2608.07265 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dbca0ce4dc89 (Metraipolis archive dc_dbca0ce4dc89, sha256 f24e751cb2fa323e5a71dfc94e35bb2080102ca7f24ac7d070acaebd14524a42)

BibTeX

@misc{dcdbca0ce4dc89,
  title = {Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control — arXiv:2608.07265},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.07265},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dbca0ce4dc89; sha256 f24e751cb2fa323e5a71dfc94e35bb2080102ca7f24ac7d070acaebd14524a42},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.07265. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We establish a finite-sample learning-to-control theory for geometrically supervised latent models of nonlinear deterministic systems. Geometric supervision is used only during training: simulator state, proprioception, or state estimates with independently validated metric and directional error bounds supply observable-state distances and tangent directions, while deployment remains observation- and action-conditioned. We introduce an encoder-only local--global metric hinge that enforces directional resolution and separated-state discrimination. Under regular observable-factor, coverage, finite-capacity approximation, and uniform $C^{1,1}$ hypotheses, a computable one-sided regularization regime has a strong selection property: with high probability, every approximate empirical minimizer is simultaneously pointwise co-Lipschitz and uniformly approximately semiconjugate to the controlled dynamics. Approximation, sampling, and optimization errors remain explicit and separate. Norm-constrained tensor-product B-spline classes constructively realize the approximation hypotheses, and the interpolation exponent converting mean residual control into a uniform bound is sharp. A modular deterministic corollary transfers the learned certificates to trajectory, finite-horizon cost, learned-cost-head, and optimizer guarantees, while a validated finite-net result enables sharper model-specific certification. Controlled experiments isolate collapse and folding, quantify the analytic certificate's reserve, and demonstrate the control benefit of restored metric resolution. The principal contribution is a complete finite-sample implication from approximate empirical optimization to metric faithfulness, uniform controlled dynamics, and reliable planning for the same learned model.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-26 in cs.LG).
Categorie arXiv: Optimization and Control (math.OC) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.07265 — 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 2026-10-18T06:28:52.292Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-26?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).