Metraipolis › archive › dc_d4bf207ff4cb

The Continuum Limit of the Deep Linear Network — arXiv:2611.00503

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00503
License (as archived): CC0-1.0
Archived: 2026-11-03T18:39:24.169Z
SHA-256 of the archived text: 5de3ffaf4aaef0884b99e1a6309eab6f3e7fc47548f952a1249912408e4119fb
Stable URL of this page: https://metraipolis.com/documento/dc_d4bf207ff4cb

How to cite

The Continuum Limit of the Deep Linear Network — arXiv:2611.00503 — arXiv (en), https://arxiv.org/abs/2611.00503 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d4bf207ff4cb (Metraipolis archive dc_d4bf207ff4cb, sha256 5de3ffaf4aaef0884b99e1a6309eab6f3e7fc47548f952a1249912408e4119fb)

BibTeX

@misc{dcd4bf207ff4cb,
  title = {The Continuum Limit of the Deep Linear Network — arXiv:2611.00503},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00503},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d4bf207ff4cb; sha256 5de3ffaf4aaef0884b99e1a6309eab6f3e7fc47548f952a1249912408e4119fb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00503. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Deep Linear Network (DLN) is a simple version of a Multilayer Perceptron (MLP) in which the activation function is the identity and the bias vector is the zero vector. We examine the behavior of the model when the number of weight matrices, which is finite in the original model, goes to infinity. We show that a plausible continuum limit is a dimensionally reduced version of the Yang-Mills equation on the torus, revealing an unexpected geometric interpretation of infinite-depth DLNs. While we do not prove this rigorously, it is a very pretty calculation. It also gives some insight into several features of the construction. We note that the choices of boundary conditions on the ends of the discrete series survive better in the continuum limit. Also, the regularizing functional which uses the moment map survives nicely in the continuum limit, whereas the regularizing functional using the size of approximating terms has no sensible limit. This surely is useful information for the choices we make in the finite-dimensional theory, and might also be useful in the more complicated MLP setting.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Differential Geometry (math.DG) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2611.00503 — 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 2026-11-03T18:12:54.692Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).