Two regimes, one objective. Closed-form merging and end-to-end distillation both reproduce each expert on its own inputs — one cheaply, one exactly.
A budget frontier. Closed-form wins under tight data, compute, or memory; distillation overtakes past ~256 examples/task. No universal winner.
When it pays. At full budget, 94.3% on ViT-L/14 matches the fine-tuned experts, and the lead grows to +9.5 at 20 tasks — precisely where a one-shot formula struggles.