The question is: How do we get LLMs to have "Eureka!" moments, on their own, when their minds are "at rest," so to speak?
The OP's proposed solution is a constant "daydreaming loop" in which an LLM is does the following on its own, "unconsciously," as a background task, without human intervention:
1) The LLM retrieves random facts.
2) The LLM "thinks" (runs a chain-of-thought) on those retrieved facts to see if they are any interesting connections between them.
3) If the LLM finds interesting connections, it promotes them to "consciousness" (a permanent store) and possibly adds them to a dataset used for ongoing incremental training.
It could work.