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The correct encoding and distance to use is of course the ones that are natural to the data -- that is to say, the latent manifold of the data. Which *is* an interpolative space for many problems (hence why deep learning models are able to generalize).
Saying "I expect the problem to be linearly interpolative in the original encoding space" is equivalent to saying "linear regression with *no* feature engineering is enough to solve any prediction problem." Which we have known to be nonsensical since long before computers existed
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A good non ML example of this is Buckingham Pi.
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