{
  "abstract": "Training datasets for upcoming LLMs would include a significant amount of AI text/image data generated from current LLMs. In such a scenario, it is important to understand how this affects batch decompositions and thereby, the performance of the resultant new LLM. In this paper, we consider AI generated data as anomalies ``linked\" to main data points and study decomposition and undersampling properties of the overall random dataset. We use redundancy graphs and iteration techniques to obtain bounds for the minimum size of a strongly dissimilar (SD) decomposition and demonstrate a phase transition phenomena, wherein the minimum size is essentially determined by the \\emph{main} data points when the number of anomalies is small and is ``taken\" over by the anomalies above a certain threshold. We also establish a size criticality result for the strong similarity of a randomly undersampled dataset and illustrate our results with examples involving categorical datasets, whose overall space size is much larger than the size of the dataset.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13201",
  "author_total": 1,
  "authors": [
    {
      "name": "Ghurumuruhan Ganesan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d19cfwh21vxmf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13201",
  "fulltext_url": null,
  "id": "d19cfwh21vxmf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13201",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Machine Learning and Data Classification"
    ]
  ],
  "openalex": "W7213312903",
  "pdf_url": "https://arxiv.org/pdf/2609.13201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d19cfwh21vxmf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies",
  "title_text": "Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/d19cfwh21vxmf",
  "venue": "arXiv",
  "versions": []
}