{
  "abstract": "Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study entropy-regulated learning under separately specified task, risk, and intervention constraints. A noise-calibrated log-determinant functional yields an exact spectral force formula and a metric decomposition into observable and prediction-null velocities. For scalar feedback, we characterize the complete interval of coefficients preserving a task-descent fraction and meeting an entropy-rate request; restricting intervention to observable directions can make that interval empty. For several protected risks, we derive an exact minimax certificate of feasibility within a specified subspace and norm budget, an exact robust extension for uncertain constraint rows, and a cone-projection formula for the entropy reduction remaining after protection. These formulas use standard convex geometry but identify when apparently active entropy control has no admissible effect. Barrier comparisons, finite-step curvature and gradient-error margins, and fresh-data audits give distinct conditional guarantees for risk thresholds. Human authority enters through the specification and release policy; the mathematics does not identify compression with alignment or certify human well-being. A memorization counterexample separates fresh-input information from sample-level information, and a noisy sample-code assumption supports a conditional generalization bound. Reproducible mathematical checks and a small real-data experiment expose both feasible interventions and failures. The resulting theory characterizes admissible entropy regulation and its limitations, rather than asserting universal accuracy or safety improvements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.22940",
  "author_total": 1,
  "authors": [
    {
      "name": "Kim Phuc Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ex72xbf3wv3qp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.22940",
  "fulltext_url": null,
  "id": "ex72xbf3wv3qp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.22940",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7162324076",
  "pdf_url": "https://arxiv.org/pdf/2605.22940",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ex72xbf3wv3qp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:43Z",
      "native_id": "2605.22940",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.22940"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints",
  "title_text": "Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/ex72xbf3wv3qp",
  "venue": "arXiv",
  "versions": []
}