A Fisher-Geometric View of Multi-Teacher On-Policy Distillation
Consolidating specialized foundation models into a unified generalist is a central goal of post-training. Two approaches are in common use: model merging, which is fast but treated as a heuristic, and multi-teacher on-policy distillation, which matches distributions but demands heavy rollout compute and suffers from cross-task gradient conflict. We show that the two are one objective seen at different orders. Within a shared basin of homologous specialists, the multi-teacher on-policy distillation objective is, to second order, exactly the Fisher-merging objective. Its minimizer is therefore the Fisher merge, a classic model-merging method given by a closed-form combination of the special...
| Authors | Liu Kaiyuan, Zhuang Ziyuan, Ma Haoxuan et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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