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In the future, AI will be capable of extrapolation, not just interpolation, i.e. broad generalization, & further, general intelligence. This is an endeavor entirely orthogonal to interpolation / curve fitting, which will be achieved through an entirely different set of techniques
Of course, interpolation & pattern recognition are nevertheless a fundamental component of intelligence -- just not the most powerful. Being able to do it well -- by refining deep learning -- is immensely valuable
But (by the same no free lunch theorems you invoke) there's NO difference between interpolation and extrapolation. To say "interpolation is a more certain generalisation than extrapolation" is to say "the data is generated by a function linear in THESE particular features".
Note: obviously you know far more about theoretical learning theory than I do, so I'm just asking what I'm missing. Under reparameterisations of feature- and target- spaces, we can switch between interpolation and extrapolation.
H. Poincaré (1908) :les faits les plus intéressants sont ceux qui peuvent servir plusieurs fois ; ce sont ceux qui ont chance de se renouveler….. Quels sont donc les faits qui ont chance de se renouveler ? Ce sont d'abord les faits simples
and ( or +): Einstein : An explanation of data should be made as simple as possible, but no simpler
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