[krona]

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

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

[kolinko]

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

The argument stands.

[krona]

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.

[memoriyato3]

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?

[krona]

> 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'.

[kolinko]

What you’re saying here makes no sense.