A fascinating thing for me after reading this is: how can it be that the "circuit input" is compatible with its output to the point where the performance improves? The training process never saw this particular connection just like it didn't see layer 60 output into layer 3 or whatever.

Great read, makes you wonder what else is encoded in these models that might be useful!

I think the intuition is that the first N layers decode into "thought language" while the last N encode back to desired output language. So if there are well defined points where it transitions between decoding/understanding, thinking, and rendering back to language, those 2 transition points should be in the same vector space of "LLM magic thinking language".