It's a tautology that for a given truth table mapping inputs to "correct" outputs there exists a function that produces that mapping. Saying that you can't tra

It's a tautology that for a given truth table mapping inputs to "correct" outputs there exists a function that produces that mapping. Saying that you can't train an LLM to NOT hallucinate is saying that it's impossible for any LLM to always produce output matching any particular truth table. There may exist truth tables where it's not possible to produce an LLM to match them (for some finite size of LLM perhaps), but my claim isn't a tautology - it's just an assertion that there exist some truth tables which an LLM can be trained to match. It may be tricky to make the LLM in the first place, but it's certainly not as tricky to verify it. You can test it with every input you consider to be present in the truth table, record its results, and throw it away if it doesn't match. The only possible results here are either non-convergeance or a "perfect" LLM. You can get rid of the non-convergeance if you bound the size of the LLM and literally iteratively verify every single possible model. The authors of the paper didn't do that. For trivially sized models and inputs, that's completely possible. For a 7B parameter model, nobody is doing that ever. But you can prove the title statement wrong with a ten-parameter model and a one-byte input.