A reason to do student-teacher distillation is that soft target logits in general are a richer medium than text that tokenizes to hard targets. More steering signal per teacher token. And running ultra large 10T tier models in autoregressive generation mode can get expensive. So there are reasons not to reduce to text only synthetics.
I agree, and if my suspicion is right, it’s rarer because it’s much easier to deploy the large LLM and filter for it’s best output than to waste time running it on arbitary output just to train the student.
Though you could argue that perhaps labs just save the per token distribution and use that during fine tuning … which starts looking more like student teacher fine tuning if not classic distillation from random weights
Full distributions are a fucking pain to save - at this point just save the hidden states. But there are lossy compression tricks there.