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It's funny but most applied mathematicians would not call interpolation generalization.
The term "generalization" means something completely different in math compared to ML.
Not really. There are different settings of course. One cool setting is these neuro-differential solvers (three body problem) etc. I think they only solve problems with local condition number <= that in the train data set.
For example, if those navier-stokes or 3body interpolators can guarantee error bounds in regions where the local condition numbers are greater than they ever saw that would be huge. I would definitely call that generalization.
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