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Common Covariance Geometry and Certification for Brownian Kernel Ladders — arXiv:2609.29525

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.29525
License (as archived): CC0-1.0
Archived: 2026-10-08T05:26:04.294Z
SHA-256 of the archived text: a7ff3030b5803a3a418faa91c112489b9420b54f32fd3ed22df2ed6f078c104c
Stable URL of this page: https://metraipolis.com/documento/dc_60c204ea080c

How to cite

Common Covariance Geometry and Certification for Brownian Kernel Ladders — arXiv:2609.29525 — arXiv (en), https://arxiv.org/abs/2609.29525 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_60c204ea080c (Metraipolis archive dc_60c204ea080c, sha256 a7ff3030b5803a3a418faa91c112489b9420b54f32fd3ed22df2ed6f078c104c)

BibTeX

@misc{dc60c204ea080c,
  title = {Common Covariance Geometry and Certification for Brownian Kernel Ladders — arXiv:2609.29525},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.29525},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_60c204ea080c; sha256 a7ff3030b5803a3a418faa91c112489b9420b54f32fd3ed22df2ed6f078c104c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.29525. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A representation-adaptive kernel class produces, on a fixed sample, a union of reproducing-kernel Hilbert-space ellipsoids rather than one ellipsoid. We introduce the minimum-trace common covariance that dominates the unrestricted empirical union generated by Brownian kernel ladders and develop its statistical, approximation-theoretic, and computational consequences. The covariance value admits exact formulations through absolutely two-summing operators and covariance-dominated multipliers, and it yields a universal Gaussian-complexity bound. A closed last-layer Dirac-trace reduction and a signed Brownian threshold representation convert the generic covariance problem into threshold, graph-coarea, and effective-resistance geometry. These tools give deterministic depth laws, conditional Gaussian reverses, random-design and perturbation transfers, and an exact empirical Kolmogorov-width formula whose leading covariance eigenspaces approximate the complete adaptive ball simultaneously. Finite contact, active semidefinite programs, verified separation, and a convex resistance-design relaxation provide complementary lower and upper certificates. A finite covariance-indexed Brownian path on frozen representations illustrates the distinction between successful covariance certification and predictive selection: all reported path certificates succeed, whereas the locked predictive study misses one predeclared aggregate criterion. The paper thereby identifies one finite-dimensional covariance object linking unrestricted kernel adaptation, Gaussian geometry, common subspaces, and certifiable computation.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-25 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.29525 — 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 2026-10-08T04:50:39.439Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).