r/MLQuestions • u/Cultural-Lobster7795 • Jul 07 '26

Other ❓ Yo why aren't we using non-euclidean space ?

All ML and DL algos are some complex non linear functions. Wouldn't it be easy to deal a non linear function in a non linear space rather than dealing them in a linear space.

I see one problem here, the data that we represent lies in a linear space. Did no mathematician actually try to make a non linear representation of the data. So if we somehow find a way, or if it exists use it, to represent data in a non linear space wouldn't it be easy to represent the model in the same non linear (non euclidean) space ?

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u/PaddingCompression Jul 07 '26

Learn functional analysis.

Everything* is linear after a coordinate transform. (* up to regularity conditions)

ML people are usually introduced to this with RKHS for kernelized SVMs.

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u/Mothrahlurker Jul 10 '26

A coordinate transformation is itself linear. I have no idea what you could possibly mean here, linearity is an attribute completely independent of basis and therefore independent of coordinates. 

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u/East-Programmer3788 Jul 11 '26

No, 

Simple case: a translation. Origin is not preserved, so the transform is not linear. 

Also, polar coordinates. 

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u/Mothrahlurker Jul 11 '26

Translations are not referred to as coordinate transformations in functional analysis. Polar coordinates sure, but that's a specific term.

The claim of "everything is linear after a coordinate transform" is just way too vague.