[perching_aix]

Undecidability is not relevant here beyond e.g. a model incorrectly claiming something is decidable, and potentially even following through. It is no different to the model incorrectly claiming anything else.

These are statistical systems, so guaranteeing any particular high level behavior is not possible because of that. But given that they're working with natural language, that was never going to happen anyways, for the obvious language theoretic reasons.

The more appreciable interpretation of the claim is that they can be nevertheless tuned so that this issue becomes practically resolved. Contending guarantees and theoreticals is simply misplaced, these are not formal symbolic reasoning systems being buggy.

[greyface-]

GP was asking for a guarantee against emitting false decidable statements. We agree that this is impossible. You can slap layers upon layers of heuristics on top, yes, but you will not eliminate all hallucinations because Church and Turing proved it fundamentally impossible nearly a century ago.

[perching_aix]

I might be slow today but I'm pretty sure that the Church-Turing thesis is about undecidable statements, not false decidable statements. If a decidable statement is false... then that's it, it is just false, that's how we can decide so in the first place.