{
  "abstract": "Csiszar's formulation of the $f$-divergence introduced a vast family of functionals for quantifying dissimilarity between probability distributions. However, many applications in statistics and information theory rely only on a few $f$-divergences, such as the Kullback-Leibler divergence, the $χ^2$-divergence, and the squared Hellinger distance. These divergences are especially useful because they admit simple compositional formulas under product measures, a property sometimes referred to as tensorization. In this work, we refine a formalism of tensorization previously introduced in the literature. Then, we show that any possible tensorization formula has a multi-affine form characterized by a single parameter, and identify all tensorizable $f$-divergences under our adopted notion of tensorization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28556",
  "author_total": 3,
  "authors": [
    {
      "name": "Rodrigo Cruz"
    },
    {
      "name": "Flavio P. Calmon"
    },
    {
      "name": "Qian Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48nn0b51kqjmc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28556",
  "fulltext_url": null,
  "id": "48nn0b51kqjmc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28556",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7204808564",
  "pdf_url": "https://arxiv.org/pdf/2608.28556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48nn0b51kqjmc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A Complete Characterization of Tensorizable $f$-divergences",
  "title_text": "A Complete Characterization of Tensorizable f-divergences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/48nn0b51kqjmc",
  "venue": "arXiv",
  "versions": []
}