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I defined cross-domain with an example. ChatGPT is not trained to practice chemistry and law, yet it can do both. It is cross-domain.

You can make it stronger at being cross domain, but it satisfies the minimum requirement.

It cannot. It doesn’t reason. Gambling and winning (1-10^N)*100% times is not the same as reasoning and providing accurate answers the same amount of times. If you reason about something, your errors fall into certain categories of fallacies often related to incomplete information. LLM hallucinations are easy to spot with reasoning, they are of statistical nature.

(1-10^N)*100% times

It is trained to practice chemistry and law. The reason it can do those because it's trained on an appreciable portion of all human output on both or those fields. If that's not training on them I don't know what is.

It is trained to practice chemistry and law

No, it is not. It is trained to predict next token, and it is trained to follow user instructions.

I mean, it a very literal sense, it is. Chemistry and law textbooks are in the training corpus. It is trained on these

This sounds backwards to me. The fact that I can show you a law book and you will be able to pass a law exam is a consequence of you being "generally intelligent". If I show these books to something less intelligent like a cow, or less general, like a CNN, they won't be able to do that.

no, you're not understanding me. I'm not making any claim on whether they're any good at those subjects, merely that they are, objectively, trained on them

What is the relevance of this claim on its own if training on something alone is not sufficient for them to practice law, and you actually have to add cross-domain into picture for it to work, making it "general"?

I still disagree though, they are not trained to practice law. They are trained to remember law, but practice come from general training to follow instructions.

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