TL;DR: a solution for LLMs of medium size already exists.
The situation would be significantly better if we could provide succinct arguments for the fact being true. The pig claim could possibly be supported by a video—though that’s not much Bayesian evidence due to forge possibility, but it might still restrict what the arguments can say about a pig, moreso if some tests are run like adding weights and so on. Many claims are harder to support with direct evidence.
The next best thing is a scalable transparent argument that your interlocutor would accept each derivation step, and finally the claim itself. For humans, this still requires communicating all derivation steps (because your peer cannot be sure if you ran a simulation of them providing any argument).
But things change for AI models: you can have a scalable transparent argument of knowledge that, after reading your book, the model would output “I believe that <your fact>, having updated to credence <P>”, which you could then use for future interactions. It requires to feed the book to the model once, sure, but the key feature in this case is that you can prove its output, including to a human; then a large class of hypotheses disappears, leaving essentially “LLM could not evaluate the arguments right” vs “all arguments are correct”.
You can, optionally, even have private sections in the book, and provide zero knowledge about its contents to verifiers besides the LLM! As for soundness, it is thought to be computationally intractable to construct a false ZK-STARK (not that it is fast to construct for actual computation, but still).
TL;DR: a solution for LLMs of medium size already exists.
The situation would be significantly better if we could provide succinct arguments for the fact being true. The pig claim could possibly be supported by a video—though that’s not much Bayesian evidence due to forge possibility, but it might still restrict what the arguments can say about a pig, moreso if some tests are run like adding weights and so on. Many claims are harder to support with direct evidence.
The next best thing is a scalable transparent argument that your interlocutor would accept each derivation step, and finally the claim itself. For humans, this still requires communicating all derivation steps (because your peer cannot be sure if you ran a simulation of them providing any argument).
But things change for AI models: you can have a scalable transparent argument of knowledge that, after reading your book, the model would output “I believe that <your fact>, having updated to credence <P>”, which you could then use for future interactions. It requires to feed the book to the model once, sure, but the key feature in this case is that you can prove its output, including to a human; then a large class of hypotheses disappears, leaving essentially “LLM could not evaluate the arguments right” vs “all arguments are correct”.
You can, optionally, even have private sections in the book, and provide zero knowledge about its contents to verifiers besides the LLM! As for soundness, it is thought to be computationally intractable to construct a false ZK-STARK (not that it is fast to construct for actual computation, but still).