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Optimal Transport Bounds for Latent Density Smoothing on MTW($K>0$) Manifolds — arXiv:2609.33629

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.33629
License (as archived): CC0-1.0
Archived: 2026-10-07T23:25:14.608Z
SHA-256 of the archived text: dff3365e1196028378199dba7f24853a5a3b08d5e8b750b697f75471297e95c3
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How to cite

Optimal Transport Bounds for Latent Density Smoothing on MTW($K>0$) Manifolds — arXiv:2609.33629 — arXiv (en), https://arxiv.org/abs/2609.33629 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dfd585d9866e (Metraipolis archive dc_dfd585d9866e, sha256 dff3365e1196028378199dba7f24853a5a3b08d5e8b750b697f75471297e95c3)

BibTeX

@misc{dcdfd585d9866e,
  title = {Optimal Transport Bounds for Latent Density Smoothing on MTW($K>0$) Manifolds — arXiv:2609.33629},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.33629},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dfd585d9866e; sha256 dff3365e1196028378199dba7f24853a5a3b08d5e8b750b697f75471297e95c3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.33629. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Smoothing an empirical distribution can fill gaps between observations, but noise added in the surrounding space also moves probability mass away from the manifold supporting the data. We study this tradeoff through Wasserstein error bounds for intrinsic heat smoothing, ambient Gaussian smoothing, and smoothing in an encoder--decoder's latent space. Under the Ma--Trudinger--Wang condition with positive cross-curvature and the stated transport-regularity assumptions, we prove that sufficiently small intrinsic smoothing improves upon the unsmoothed empirical measure. Our ambient bound quantifies how increasing the surrounding dimension restricts the smoothing scale suggested by the bound. For latent smoothing, the analysis shows how the benefit depends on reconstruction accuracy and on how the encoder--decoder pair preserves movement along the manifold and responds to noise in other directions. A quadratic approximation to the bound yields bandwidth-selection rules and conditions favoring latent smoothing in this comparison. Controlled synthetic experiments examine the predicted bandwidth and geometric trends. An exploratory MNIST study illustrates latent smoothing relative to pixel-space perturbations.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.33629 — 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 2026-10-07T23:04:09.492Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).