I imagine a huge slender cylindrical (whatever shape) “database” existing at the center, and “linear thoughts” would be a data stream that would propagate from this central position, but remain connected to it, like a small tendril. This tendril would be 1 conversation, or a line of thought, similar to the stream of consciousness literary device.

When that instance, conversation, thought, etc. is deemed “complete”, either by outside environment or internal timers, this tendril will fold itself perfectly back into that center database, allowing the AI to “re-center” itself, seamlessly (once systems have been perfected) integrating the most recent information into its already existing database, and allowing it to bring that entire knowledge base into the next virtual space it occupies.

Hope this helps!