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Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions — arXiv:2610.01472

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01472
License (as archived): CC0-1.0
Archived: 2026-10-06T15:33:01.273Z
SHA-256 of the archived text: 3fd375a915e0a6b165b3febe8d82d719908b69f4760cf14de384a3ffa04e9ab9
Stable URL of this page: https://metraipolis.com/documento/dc_cdb01acd884c

How to cite

Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions — arXiv:2610.01472 — arXiv (en), https://arxiv.org/abs/2610.01472 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cdb01acd884c (Metraipolis archive dc_cdb01acd884c, sha256 3fd375a915e0a6b165b3febe8d82d719908b69f4760cf14de384a3ffa04e9ab9)

BibTeX

@misc{dccdb01acd884c,
  title = {Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions — arXiv:2610.01472},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01472},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cdb01acd884c; sha256 3fd375a915e0a6b165b3febe8d82d719908b69f4760cf14de384a3ffa04e9ab9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01472. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Comparing two high-dimensional discrete distributions has always been a challenging task due to the exponentially growing state space and complex changes in interactions. A recent work suggests comparing distributions through a vector field trained using flow matching between two continuous distributions. The resulting vector field at mid-point vanishes if and only if two distributions identical. However, such a flow-based criterion does not naturally apply to discrete distributions. We extend this principle to the discrete domain and introduce the \emph{Zero Flux} criterion, a discrepancy based on local probability fluxes. Under independent coupling, we show that all local probability fluxes vanish at the midpoint if and only if two distributions are the same. This discrepancy decomposes the joint distributional difference into smaller, local contributions and can be efficiently estimated from samples. We establish finite sample error bounds for our estimator. Experiments on synthetic and real categorical data demonstrate reliable recovery of sparse dependence signals and stable tracking of distribution shifts in high dimensions.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-10-02 in stat.ML).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.01472 — 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 2026-10-06T15:12:55.875Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).