{
  "abstract": "Under the parametric loss L(N,D) = E + A/N^α + B/D^β with training compute C = 6ND, I derive the compute-optimal model size and token count in closed form: N* = G(C/6)^{β/(α+β)} with G = (αA/(βB))^{1/(α+β)}. I prove that the constrained problem is strictly convex in log N, so the solution is unique, and derive a quadratic approximation to the loss from misallocation. Two published fits are evaluated: the rounded constants of Hoffmann et al. (2022) and the re-estimate of Besiroglu et al. (2024), both read directly from the papers' text. They imply different allocation rules. At the Gopher budget of 5.76 × 10²³ FLOPs, the first gives N* = 32 B parameters and 93 tokens per parameter; the second gives N* = 72 B and 18 tokens per parameter. The ratio drifts with compute in opposite directions under the two fits (50 → 153 against 22 → 16 tokens per parameter over 10²¹–10²⁶ FLOPs). Misallocation is cheap near the optimum: a model 2× too large raises loss by about 0.005 nats, and offsetting a 4× oversize needs 1.8–1.9× more compute. The prescriptive content of \"compute-optimal\" depends on second-decimal differences in fitted exponents.",
  "abstract_shown": true,
  "affiliations": [
    "Former Officer, Chaitanya Godavari Grameena Bank (CGGB)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Manoj Kumar Aguru"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brx0154jczwqw.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23450087",
  "fulltext_url": null,
  "id": "brx0154jczwqw",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23450087",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23450087/files/11_ai_compute_optimal_scaling.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brx0154jczwqw.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:13Z",
      "native_id": "23450087",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23450087"
    }
  ],
  "subjects": [],
  "title": "Compute-Optimal Allocation Between Model Size and Data Under a Parametric Scaling Law: Closed-Form Solution, Convexity Proof, Misallocation Penalty, and Sensitivity to the Fitted Constants",
  "title_text": "Compute-Optimal Allocation Between Model Size and Data Under a Parametric Scaling Law: Closed-Form Solution, Convexity Proof, Misallocation Penalty, and Sensitivity to the Fitted Constants",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:13Z",
  "url": "https://research.draconitic.com/paper/brx0154jczwqw",
  "venue": "Zenodo",
  "versions": []
}