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[Submitted on 1 Oct 2026] Title:Token Utility for On-Policy Distillation via Local Trust-Region Optimization View a PDF of the paper titled Token Utility for On-Policy Distillation via Local Trust-Region Optimization, by Narayanan Sadagopan and 2 other authors View PDF HTML (experimental) Abstract:Token-selection methods for on-policy distillation (OPD) prioritize student-visited positions using diverse signals, including uncertainty, teacher-student disagreement, and mismatch direction. We instead derive token importance from the distillation objective itself: how much can each position's loss decrease under an equal local KL budget on the student's predictive distribution? The answer is the utility $s_t=g_t^\top F_t^\dagger g_t$, where $g_t$ is the logit gradient and $F_t$ is the categorical Fisher matrix. For reverse-KL it equals the student-weighted variance of the student-teacher log-probability ratio, and for forward-KL it equals the Pearson $\chi^2$ divergence, so the appropriate utility follows from the choice of objective. On shared training checkpoints, several independently motivated criteria, including student entropy, KL disagreement, and TIP, concentrate their importance on nearly the same positions as the derived utility at a 50\% selection fraction, while diverging at stricter fractions and for direction-specific criteria. We instantiate the utility as Fisher Utility Weighting (FUW), a continuous, mean-normalized token weighting. Across seven mathematical reasoning benchmarks and three Qwen3 student-teacher pairs, FUW improves over matched uniform OPD under both reverse-KL (1.35-4.0 macro points) and forward-KL (1.08-2.71 macro points), and is competitive with existing selective methods using a single closed-form score derived from the training objective. Comments: 10 pages, Accepted to Pre-to-Post workshop at NeurIPS 2026 Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) Cite as: arXiv:2610.18883 [cs.LG] (or arXiv:2610.18883v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2610.18883 arXiv-issued DOI via DataCite (pending registration) Submission history From: Narayanan Sadagopan [view email] [v1] Thu, 1 Oct 2026 20:01:20 UTC (1,992 KB) Full-text links: Access Paper: View a PDF of the paper titled Token Utility for On-Policy Distillation via Local Trust-Region Optimization, by Narayanan Sadagopan and 2 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG new | recent | 2026-10 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)