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Comment by mellosouls | Hacker News Reader

Let L(uy,y) = fy denote a parametric partial diﬀerential equation with y being a parameter from a high-dimensional parameter space Y ⊆ Rp and uy the associated solution in a Hilbert space H. After a high-ﬁdelity discretization...

These AI folks are clearly very clever, but they don't actually believe that's got anything to do with how human thinking works, right?

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Whenever I see "Hilbert space" remarks in a paper that doesn't concern abstract math, I roll my eyes and imagine a chef who starts his youtube video with "Today we are going to cook a salad. For better precision, we are going to use knifes of triangular shape, three dimensional plates of circular shape, and the 100% dihydrogen of oxyde solution." All this only to obfuscate the fact that the entire recipe is just chopping a few carrots.

Try doing quantum mechanics, even at beginners level, without a proper knowledge of Hilbert spaces.

the subclass of "Reproducing kernel Hilbert spaces" form the basis for a large class of ML algorithms (kernel methods)

It's literally called "the mathematics of ARTIFICIAL intelligence"

The important word is intelligence.

Research on natural intelligence or general intelligence presents itself as such.

AI leaders occasionally seem to pontificate on AGI, yet it's difficult for a layperson like me to see how their expertise (as seen in publications like this) translates.

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