EDIT: also there's a reason the dial is called "effort", not "smarts".
Of course I don't know if there's really a way for this to be molded in current LLM's (sounds more like diffusion)
They work on a problem until their brain is full of problem-related concepts. Then something comes. After validation it might be a solution.
See, this insight it had early on looked like a red hering for a while, but then turned out to be load-bearing. And that's not just a difference in semantics, it changed the whole conclusion (spoiler: it didn't). And Claude is very eager to tell you about this exciting journey