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The only form of generalization you can do with a parametric curve (like a DL model) is interpolation, by construction. The way DL solves "extrapolative" problems is by first turning them into interpolative problems, which requires a dense sampling of the data manifold...
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?
Extremely insightful thread. One of the first research problems I encountered turned out to be much easier to solve after sorting. During a discussion with my advisor, my naive suggestion to make it an "end-to-end ml solution" was struck down by this simple question:
"How do you think Neural nets can learn how to sort?" I also wrote about it here:https://twitter.com/parthsh_/status/1411895057305653255?s=20 …
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