I think it depends on the use. The kind of AI you're suggesting wouldn't need to ingest the entirety of every book and movie you've seen, it would just need to

I think it depends on the use. The kind of AI you're suggesting wouldn't need to ingest the entirety of every book and movie you've seen, it would just need to store a summary and a location for the original file. It's legal for me to make digital copies of copyrighted works I own so long as they're not redistributed. If I have a local AI maintaining my personal data for reasons other than generating competing works, that shouldn't involve copyright at all.