When Top-K Misses the Decision: Tool-Call Drift in Multi-Teacher On-Policy Distillation

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arXiv:2607.07050v5 Announce Type: replace-cross Abstract: Top-$K$ teacher logits make on-policy distillation tractable, but retained teacher mass does not certify student-relative gradient fidelity. We study routed, two-teacher tool-use distillation. In a frozen Qwen3.5-9B audit, the tool teacher ranks the entry token first on 500 tool prompts, and top-32 reinforces it in every matched pair. The response teacher's top-32 instead retains 99.99\% mass yet contains the same token on only 0.4\% of 500 response prompts; student-aware support restores the coordinate in all matched pairs and nearly matches full-vocabulary descent. On the tool route, top-32 preserves the reinforcing direction but substantially attenuates its full-vocabulary magnitude despite mass displayed as 1.000000. Matched restoration connects the response-side omission to behavior: restoring the entry coordinate at every supervised response position lowers full-generation over-calling from $14.2 \pm 2.1\%$ to $3.7 \pm 0.5\%$ across three seeds, but also lowers call recall by 12.4 points. A non-tool placebo changes over-calling by only 0.95 points. A synthetic output-logit-gradient-matched reroute also fails to reproduce exact restoration. We compare three optimization layers: student-aware support changes distilled coordinates, loss shaping changes retained-signal strength, and validation-tuned entry bias shifts inference without retraining. They expose distinct trade-offs in correction scope, system access, and required-call retention. Llama-3.1-8B reproduces the directional support asymmetry under its …

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