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A Constructive Orbit-Based Theory of Learnability — arXiv:2610.41641

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41641
License (as archived): CC0-1.0
Archived: 2026-11-03T05:40:54.455Z
SHA-256 of the archived text: c67f6fc3b4c88c0d45cff72311e8de666d47ec59cb2683863dceb7046ffd54df
Stable URL of this page: https://metraipolis.com/documento/dc_43cedbfe8cf5

How to cite

A Constructive Orbit-Based Theory of Learnability — arXiv:2610.41641 — arXiv (en), https://arxiv.org/abs/2610.41641 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_43cedbfe8cf5 (Metraipolis archive dc_43cedbfe8cf5, sha256 c67f6fc3b4c88c0d45cff72311e8de666d47ec59cb2683863dceb7046ffd54df)

BibTeX

@misc{dc43cedbfe8cf5,
  title = {A Constructive Orbit-Based Theory of Learnability — arXiv:2610.41641},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41641},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_43cedbfe8cf5; sha256 c67f6fc3b4c88c0d45cff72311e8de666d47ec59cb2683863dceb7046ffd54df},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41641. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop a finite-dimensional orbit framework for constructing data-adapted dictionaries, sparse realizations, and predictive extensions. The method uses wrapped weighted shifts to generate orbit dictionaries and local interpolation maps from independent orbit representatives, turning the learning problem into three explicit tasks: scaffold discovery, sparse realization on the discovered dictionary, and prediction through learned sparse coordinates. We introduce CCDS as the main constructive ingredient: a deviation-controlled sparse realization procedure that recovers MP/OMP-type behavior at the minimal-deviation boundary while allowing feasible interior paths with prescribed residual geometry that is inaccessible to MP/OMP. We prove generic orbit independence, exact block interpolation with norm control, observable bounds on sparse approximation distortion, sparse realization guarantees on selected supports, and fixed-path stability under admissible perturbations of the block interpolants. These results connect sparse approximation, interpolation, and finite-dimensional operator dynamics through the construction and analysis of data-induced orbit dictionaries. Experiments on synthetic geometry, controlled realization tests, and standard classification benchmarks show that selected orbit scaffolds have substantially better matched-rank projection behavior than random orbit or unstructured alternatives, that CCDS attains near-zero realization error at the minimal-deviation boundary, and that predictors trained from the sparse CCDS certificates give competitive performance.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.41641 — 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 2026-11-03T05:26:25.702Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).