{
  "abstract": "Reverse and forward Kullback--Leibler (KL) divergences provide complementary supervision in on-policy distillation: reverse KL refines the student's active token rankings, and forward KL allocates mass to teacher-supported candidates. At student-generated prefixes, we form a four-observation matrix by treating the student and teacher as both candidate sources and evaluators. The diagonal self-observations measure uncertainty, while source-centered cross-observations recover the two KL objectives. We establish an exact identity equating the Fisher inverse-metric coupling of their logit gradients with the sum of these contrasts, yielding a common local descent direction for distinct positive distributions. Observation-coordinated on-policy distillation (OC-OPD) uses observations to set preferences, closed-form bargaining to coordinate gradients, and distributional discrepancy to scale the update. Across three heterogeneous student settings (non-thinking generation, thinking generation, and base-model initialization), OC-OPD achieves strong gains in mathematical reasoning and transfers effectively to out-of-distribution scientific question answering and code generation. Our code is publicly available at: https://github.com/RuoranXu/OC-OPD.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01965",
  "author_total": 4,
  "authors": [
    {
      "name": "Ruoran Xu"
    },
    {
      "name": "Yilun Zhao"
    },
    {
      "name": "Ziyu Chen"
    },
    {
      "name": "Arman Cohan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1ss2qtex55vr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01965",
  "fulltext_url": null,
  "id": "d1ss2qtex55vr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01965",
  "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",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1ss2qtex55vr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "OC-OPD: Observation-coordinated Supervision for On-Policy Distillation",
  "title_text": "OC-OPD: Observation-coordinated Supervision for On-Policy Distillation",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/d1ss2qtex55vr",
  "venue": "arXiv",
  "versions": []
}