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[Submitted on 17 Aug 2026] Title:A Shared Learning Rate Is Not a Neutral Control in Selective On-Policy Distillation View a PDF of the paper titled A Shared Learning Rate Is Not a Neutral Control in Selective On-Policy Distillation, by Chencheng Zhu View PDF HTML (experimental) Abstract:Selective on-policy distillation trains a student only at the token positions a selector scores highest, and the literature compares selectors under a single shared learning rate--a control chosen to be neutral. We show it is not. Under LoRA on GSM8K (Qwen2.5-1.5B student, 7B teacher), across an 8x learning-rate grid, dense supervision is statistically flat (swing 1.8 pp, p=0.26) while every selective arm moves with the rate: 5.4 pp for a random 5% subset, 6.7 pp for a total-variation selector, up to 17.7 pp for a teachability selector. Consequently the dense-versus-selective verdict reads 10.1 pp at lr=1e-4 but 5.1 pp at 5e-5--a 2.0x difference decided by a parameter the protocol treats as scenery--and two of six pairwise significance calls between selectors flip between adjacent rates without any rank inversion. We call this selector-rate entanglement and trace it to selection itself rather than step size: AdamW update magnitudes track the rate to within 2.2% despite 15.5x gradient-norm differences across arms. A preregistered frozen-scoring ablation (selection scored by the initial student; criterion, budget, and on-policy rollouts unchanged; 12 seeds per cell) shows live scoring adds 3.79+/-1.69 pp of rate sensitivity (p=0.035) while the frozen arm remains significantly entangled (p=0.015): the feedback loop aggravates the phenomenon rather than causing it. Under full fine-tuning at the rates this literature actually uses (1e-6 to 1e-5) the pattern grows: dense itself swings 19.8 pp, the selective arm 49.5 pp, and the verdict ranges from a non-significant +3.6 pp at the published operating point to +34 pp (p=0.005) one notch hotter. On MATH-500 the rate dependence does not reproduce under LoRA, scoping that result, while the ~10 pp cost of selective training does. We prescribe reporting the arm x rate matrix, not a shared-rate column, as a precondition for selector comparisons. Comments: 16 pages, 3 figures, 6 tables Subjects: Machine Learning (cs.LG) Cite as: arXiv:2609.22109 [cs.LG] (or arXiv:2609.22109v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.22109 arXiv-issued DOI via DataCite Submission history From: Chencheng Zhu [view email] [v1] Mon, 17 Aug 2026 03:35:00 UTC (51 KB) Full-text links: Access Paper: View a PDF of the paper titled A Shared Learning Rate Is Not a Neutral Control in Selective On-Policy Distillation, by Chencheng Zhu View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs 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?)