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To do actual extrapolation from a few samples, you need a discrete model (like a computer program), not just a parametric curve. A simple example you can play with to understand the difference is list sorting: try to solve it either via program synthesis or via a DL model.
You can use 2-3 ex to synthesis a discrete program that will work with any possible list of ints, in any range, of any length. With DL, you'll need to first make the problem interpolative: train on millions of lists, then can only generalize to lists of similar length / ranges
So how can we deal with the extrapolation problems and solve the causation, and not the correlation? Is there any algorithms for solving these problems or we have only program synthesis?
using the same arguments as yours, I can say it extrapolates, not the otherwise.
@fchollet Do you know if people have had any success formulating sorting as an RL problem? It seems like it should be easy to learn bubble sort by having a "Roomba" that just flips out-of-order pairs.
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