Earlier quoted context omitted.
I don't see much similarity? Unless you're looking at self-distillation in general and not just this use of it.
How not? I think the analogy is actually pretty specific to this paper, not just self-distillation in general. During sleep your brain replays experiences but noisy and distorted. The replays are often incoherent as narratives (dreams are weird). But the consolidation still works because the value isn't in the narrative coherence, it's in the activation patterns at each moment. Important pathways get strengthened, we…
Self-distillation shifts the behavior of the model towards that of the model + steering. As such, you don't strictly "need" the tokens to be in-domain for it to work. The logits are a vessel for transferring the steering into the model's internals.
The tokens can be gibberish. What transfers isn't whether they're gibberish or not, but how the flavor of model predictions, if given gibberish, differs from that of an unsteered version of itself.
In this specific case, the behavioral difference comes from the "temperature-shifted, truncated samples" in the "teacher" sampling strategy, and it is that difference that is internalized by the "student" model.