{
  "abstract": "Solomonoff induction is a general solution for sequence prediction that started the field of algorithmic information theory around 1960. Let $M$ be the universal semimeasure. After observing a string $ω_1 \\cdots ω_{n-1}$, it predicts the next bit $ω_n$ to be $b$ with conditional probability proportional to $M(ω_1 \\cdots ω_{n-1} b)$. Thus the error of this probability is \\[ e_ω(n) = 1 - \\frac {M(ω_1 \\cdots ω_{n-1}ω_n)} {M(ω_1 \\cdots ω_{n-1} 0) + M(ω_{1} \\cdots ω_{n-1} 1)}. \\] If $ω$ a computable infinite sequence with a self-delimiting description of at most $k$ bits, then $\\sum_n e_ω(n) \\le k\\ln 2+O(1)$. Lattimore, Hutter and Gavane consider the problem of predicting computable patterns in a sequence, for example, the pattern of repeated bits $ω= 00\\,11\\,00\\,00\\,11\\,00\\cdots$ They show that the error probabilities of the bits fixed by a computable pattern have limit zero, for example, for repeated bits, one has $\\lim_n e_ω(2n) = 0$. We show that for some computable pattern, the sum of $e_ω(n)$ over positions $n$ from the pattern is not bounded. However, the sum of squares $(e_ω(n))^2$ is bounded exponentially in the program length of the pattern. It is also shown that bits of $ω$ that are fixed by a computable classification function $f:\\{0,1\\}^* \\rightarrow \\{0,1\\}$, converges faster: the sum of $(e_ω(n))^2$ is bounded by a polynomial in the program length for programs whose runtime is bounded by any fixed computable time bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18632",
  "author_total": 2,
  "authors": [
    {
      "name": "Bruno Bauwens"
    },
    {
      "name": "German Kuznetsov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dns32g73gnnby.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18632",
  "fulltext_url": null,
  "id": "dns32g73gnnby",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18632",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7221824330",
  "pdf_url": "https://arxiv.org/pdf/2610.18632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dns32g73gnnby.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18632"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Solomonoff induction of selected bits and online classification",
  "title_text": "Solomonoff induction of selected bits and online classification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/dns32g73gnnby",
  "venue": "arXiv",
  "versions": []
}