A Shared Learning Rate Is Not a Neutral Control in Selective On-Policy Distillation
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 ...
| Authors | Chencheng Zhu |
|---|---|
| Primary category | cs.LG |
| Published | 17 August 2026 |
| Last updated at source | 17 August 2026 |
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