{
  "abstract": "The introduction of machine learning methods has led to significant advances in automation, optimization, and new discoveries in various fields of science and engineering. However, their widespread application faces a fundamental limitation: the models are inapplicable to different data types, and they typically lack rigorous mathematical justification. A key problem is the lack of formal criteria to ensure that a model trained on one data type will retain its properties on another. This paper proposes a solution to this problem by formalizing the concept of “analogy” between datasets and models using first-order logic and Hoare logic. We formulate and prove theorems that establish necessary and sufficient conditions for analogy in the problem of knowledge transfer between machine learning models. A practical test of the analogy theorem on simulated data obtained using the Monte Carlo method, as well as on MNIST and USPS data, showed that the MLP + MDM model demonstrates a classification accuracy of 0.874 on Source MLP MNIST, while it achieves 0.915 on Target and Hybrid.",
  "abstract_shown": true,
  "affiliations": [
    "College of New Materials and Nanotechnologies, National University of Science & Technology (MISIS)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Nikitin Nikita"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f9p8n9eyssj7.bib",
  "cited_by": 0,
  "doi": "10.1038/s41598-026-62447-w",
  "fulltext_url": "https://doi.org/10.1038/s41598-026-62447-w",
  "id": "7f9p8n9eyssj7",
  "issns": [
    "2045-2322"
  ],
  "landing_url": "https://doi.org/10.1038/s41598-026-62447-w",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "Q"
    ],
    [
      "lcc",
      "R"
    ],
    [
      "openalex",
      "1702|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7169857197",
  "pdf_url": "https://www.nature.com/articles/s41598-026-62447-w_reference.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/7f9p8n9eyssj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:45:59Z",
      "native_id": "cc40195a60814a4db78ea4d3af33dab3",
      "source": "doaj",
      "url": "https://doi.org/10.1038/s41598-026-62447-w"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "lcc:R",
      "subfield": "general"
    }
  ],
  "title": "The analogy theorem in Hoare logic for formal verification of knowledge transfer in machine learning",
  "title_text": "The analogy theorem in Hoare logic for formal verification of knowledge transfer in machine learning",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:45:59Z",
  "url": "https://research.draconitic.com/paper/7f9p8n9eyssj7",
  "venue": "Scientific Reports",
  "versions": []
}