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A pullback-corrected scalar auxiliary variable optimizer with momentum and adaptive mobility — arXiv:2609.13569

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.13569
License (as archived): CC0-1.0
Archived: 2026-10-16T00:12:48.796Z
SHA-256 of the archived text: a5c3b8d76ab4fad5d627eb58ea8cb7f262d17850a134d3e52ed38cedb54d7264
Stable URL of this page: https://metraipolis.com/documento/dc_5bc00a54e555

How to cite

A pullback-corrected scalar auxiliary variable optimizer with momentum and adaptive mobility — arXiv:2609.13569 — arXiv (en), https://arxiv.org/abs/2609.13569 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5bc00a54e555 (Metraipolis archive dc_5bc00a54e555, sha256 a5c3b8d76ab4fad5d627eb58ea8cb7f262d17850a134d3e52ed38cedb54d7264)

BibTeX

@misc{dc5bc00a54e555,
  title = {A pullback-corrected scalar auxiliary variable optimizer with momentum and adaptive mobility — arXiv:2609.13569},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.13569},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5bc00a54e555; sha256 a5c3b8d76ab4fad5d627eb58ea8cb7f262d17850a134d3e52ed38cedb54d7264},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.13569. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Objectives in scientific machine learning are often prescribed as a sum of several terms, such as the residual, boundary, initial, and data losses of a physics-informed neural network. In the pullback-corrected scalar auxiliary variable (PB--SAV) method, one scalar tracks the shifted objective while the component gradients build a positive semidefinite curvature correction of rank at most the number of components. We carry that correction into an optimizer with momentum and an adaptive mobility, applying it to the gradient and the stored momentum in a single implicit solve. A mobility that is nonincreasing in the Loewner order yields an exact modified energy law, covering Euclidean and AMSGrad-type choices; the corresponding identity for momentum appended after the solve carries a cross term of indefinite sign. For a fixed mobility we give a necessary and sufficient condition for local stability at a stationary point, depending on the Hessian minus twice the correction, and show that it also gives local geometric convergence for every scalar relaxation sequence. The implicit solve reduces to a dense system whose order is the number of components. In the forward Burgers comparison, four components reduce the mean tail objective by 64.7% and the final solution error by 50.2% relative to one component at the same learning rate and momentum settings.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-15 in cs.LG).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.13569 — 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 2026-10-15T23:54:14.851Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).