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, weak ones get pruned. Section 4.4 of this paper is what makes the connection click. They cranked training temperature to 2.0 with no truncation. 62% of the sampled outputs had no extractable code. Coherent Python that devolves into multilingual gibberish halfway through. The model still improved (+5.7pp pass@1).
This makes no sense if you think the model is learning from good code examples. But it makes a lot of sense if you think of it as the model replaying its own knowledge back to itself in a noisy/distorted form, and the replay process strengthening what matters (sharp distributions at "lock" positions where one token is correct, broad distributions at "fork" positions where multiple approaches work) while pruning what doesn't (distractor tails). The model doesn't learn anything new. It just wakes up performing better because what it already knew got cleaned up.
How is this comment not at number 1??
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.
I.e sleep replays don’t need to replay Tuesday’s meeting accurately. They just need to activate the relevant pathways so that the strong ones fire and the weak ones don’t. The pattern of what fires versus what doesn’t is the signal. The “content” of the dream is basically irrelevant.