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As far as current machine learning is concerned, generalization originates from the ability to learn the latent manifold on which the training data lies, i.e. the ability to interpolate between training samples (local generalization, by definition)
As such, attempting to study generalization by fitting models to random data is a category error, since such data offers no possibility of generalization. To understand generalization, you must look at the relationship between models and natural data manifolds.
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
Is there anything in this Universe that cannot be conceived of as an interpolation?
Having observed no data from inside a black hole, we can nonetheless make inferences about what must be going on there. But to do this, we extrapolate our physical theories beyond the observed range
I’m a fan of Roman history and I follow multiple accounts related to that. I suddenly saw Cicero talking about ML and I was like “What the f*%k”. Then I saw the name and it all made sense 
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Would you be able to share some of the hypotheses on the types of latent manifolds we could create or induce in models? Tolman-Eichenbaum machine seems interesting?
Isn't generalization already an extrapolation? After which the model can interpolate. Isn't THIS the "learning" that happens?
"learning" is just converting sample signals into a more efficient form... matrix factorization is "learning"...
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