{
  "abstract": "The classical information bottleneck (IB) measures the relevance of a representation $U$ of $X$ to a target $Y$ by $I(U;Y)$, which does not directly characterize the error of downstream decisions. For a binary hypothesis $Y$ inferred from many separately encoded observations, the optimal error exponent is the Chernoff information between the two conditional distributions of $U$ given $Y$. We study the mutual information constrained Chernoff bottleneck, which seeks an encoder that maximizes this Chernoff information subject to a rate constraint $I(U;X) \\leq R$. We show that its optimal value $C(R)$ increases strictly up to $R = H(V)$, where $V$ merges the symbols of $X$ with equal likelihood ratio, remains at the uncompressed exponent beyond, and, unlike the IB curve, need not be concave. We further show that $k+1$ outputs suffice to attain $C(R)$, where $k$ is the cardinality of $V$. We propose an alternating algorithm that updates the encoder via a generalized Blahut--Arimoto algorithm and the Chernoff parameter $s$ via a nonlinear equation, and prove that its iterates remain feasible, with nondecreasing and convergent Chernoff information. Comparing with the classical IB for $n$ samples, we show that, whenever the two objectives disagree, the IB encoder has the smaller equivocation $H(Y|U^{n})$ at $n = 1$, whereas the Chernoff bottleneck has the smaller error probability and equivocation for all large $n$. Numerical experiments confirm the theory, and on real topic-detection data from the 20 Newsgroups corpus, compressing each word to only $17\\%$ of its entropy retains $90\\%$ of the error exponent and nearly the accuracy of the uncompressed classifier.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37994",
  "author_total": 2,
  "authors": [
    {
      "name": "Dier Tang"
    },
    {
      "name": "Guangyue Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5s7c6pchx0xtk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37994",
  "fulltext_url": null,
  "id": "5s7c6pchx0xtk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37994",
  "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": [
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      "math.IT"
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      "arxiv",
      "math.OC"
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      "math.ST"
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      "openalex",
      "1705|Distributed Sensor Networks and Detection Algorithms"
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  "openalex": "W7215133726",
  "pdf_url": "https://arxiv.org/pdf/2609.37994",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5s7c6pchx0xtk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2609.37994",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37994"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Mutual Information Constrained Chernoff Bottleneck",
  "title_text": "Mutual Information Constrained Chernoff Bottleneck",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/5s7c6pchx0xtk",
  "venue": "arXiv",
  "versions": []
}