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Knowledge as Orbit: Finite Collections as Phases of an Exactly Periodic Latent Generator — arXiv:2609.17417

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.17417
License (as archived): CC0-1.0
Archived: 2026-10-15T22:40:13.238Z
SHA-256 of the archived text: a4b932554abb5e38215bd5f72820ea61ec6ec8749ad8f956c7c4de467e9feced
Stable URL of this page: https://metraipolis.com/documento/dc_e481ce5641ed

How to cite

Knowledge as Orbit: Finite Collections as Phases of an Exactly Periodic Latent Generator — arXiv:2609.17417 — arXiv (en), https://arxiv.org/abs/2609.17417 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e481ce5641ed (Metraipolis archive dc_e481ce5641ed, sha256 a4b932554abb5e38215bd5f72820ea61ec6ec8749ad8f956c7c4de467e9feced)

BibTeX

@misc{dce481ce5641ed,
  title = {Knowledge as Orbit: Finite Collections as Phases of an Exactly Periodic Latent Generator — arXiv:2609.17417},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.17417},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e481ce5641ed; sha256 a4b932554abb5e38215bd5f72820ea61ec6ec8749ad8f956c7c4de467e9feced},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.17417. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Finite knowledge is usually stored extensionally, one code or vector per item. We ask whether a finite collection can instead be stored intensionally, as the decoded orbit of one compact law that returns exactly to its start. For X objects, we encode item i as the i-th phase of a fixed rotation in a learned latent space and decode all phases with a shared network; the latent advances through a bank of rotations at integer harmonics of the cycle, a real discrete Fourier operator, so that R^X equals the identity and exact closure is guaranteed rather than learned. Images are a controlled carrier; looping video is the case where the phase order is the content's own temporal structure. Holding the decoder fixed and varying only the operator, a general learned operator diverges, a norm-preserving but non-periodic one degrades around the loop, and the exactly periodic operator is flat; on real images the gap widens. Capacity is then the decoder's budget: dense decoders carry a structural overhead per crisp image that no size reconciles with compression, while a small convolutional decoder on objects that share a manifold reaches crisp and compressed. A codebook control shows the generative law is free in reconstruction terms while multiplying the latent store many-fold. On seven benchmark clips, against a matched frame-index baseline, the cycle reaches equal or better fidelity at equal parameters while wrapping at machine precision, where the baseline leaves a visible seam; pinning the baseline's frequencies to loop harmonics closes its seam too, confirming that exact periodicity is the operative constraint. Finite cyclic knowledge can be stored as dynamics rather than independent instances, with exact recurrence supplied by algebra and content by a shared decoder.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-16 in eess.IV).
Categorie arXiv: Machine Learning (cs.LG) ; Computer Vision and Pattern Recognition (cs.CV); Image and Video Processing (eess.IV).
Pagina del lavoro: https://arxiv.org/abs/2609.17417 — 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 2026-10-15T22:18:16.511Z dalla pagina https://arxiv.org/catchup/eess.IV/2026-09-16?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).