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> They construct space between the points and extrapolate outside of the points.

They don't. They interpolate between the points on a manifold.

Manifold vs space - yes, I meant manifold, english is not my first language and I missed this word.

The argument stands.

Interpolation vs extrapolation? It's very simple distinction and fundamental. Look at ARC-AGI-3 for empirical evidence, if that's important to you. My point however is purely an a priori one.

so the proof to the unit-distance problem was on the manifold, given it was outputed by a LLM?

is the proof to the Riehmann hypothesis also somewhere on the manifold and we just need to prod the LLM with the right prompt so it locates the point?

> so the proof to the unit-distance problem was on the manifold, given it was outputed by a LLM?

By design this must be the case, even when you account for stochastic sampling i.e. 'temperature'. All it's outputs are a highly-dimensional combinatorial interpolation (I'm talking about GPTs here)

That's probably why Claude is very good at producing plausible nonsense rather than the often correct response of 'I don't know'.

What you’re saying here makes no sense.

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