“What Does Privileged Information Add to On-Policy Self-Distillation?” The usual idea is that self-distillation works because the teacher sees a worked solution, then uses that extra knowledge to better supervise the student. This paper shows much of the gain happens even without the solution. A thinking-enabled teacher can simply look at the student’s own direct responses and tell it which next-token choices it would make differently. Because both modes share the same model parameters,…