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What are the main theorems in Machine (Deep) Learning?

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2021-06-19 18:30:04

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Al Rahimi has recently given a very provocative talk in NIPS 2017 comparing current Machine Learning to Alchemy. One of his claims is that we need to get back to theoretical developments, to have simple theorems proving foundational results.

When he said that, I started looking for the main theorems for ML, but could not find a good reference making sense of the main results. So here is my question: what are the current main mathematical theorems (theory) in ML/DL and what do they prove? I would guess Vapnik's work would go somewhere here. As an extra, what are the main theoretical open problems?

As I wrote in the comments, this question seems too broad to me, but I'll make an attempt to an answer. In order to set some boundaries, I will start with a little math which underlies most of ML, and then concentrate on recent results for DL.

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