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> It explains in informal terms the structure and mechanics of a CNN

It actually gets quite formal. you could implement a (non-performant) CNN from everything in that video. The point is, that someone came up with a hypothesis "hey imposing this structure should yield faster convergence to usable results" is totally inductive science, and that is able to be explained quite well and simply from simple primitives that you don't need a math degree to understand really indicates some level of maturity in the field.

>People are hoping to see, ultimately, mathematical proofs that neural networks can e.g. efficiently learn target functions given a certain amount of training data and a certain number of trainable parameters.

yeah I don't dispute that, but to characterize our understanding of machine learning as not going beyond 3 or 4 neurons is just plain crazy.

Moreover, for some RNNs, e.g. character-based LSTMs trained on language models, we can extract feature details. I recall one case (sorry not bothered to find it) where there was a memory line dedicated to detetcting opening and closing quotation marks. Now this is a feature that one would expect to be obvious, or at least more so than other language features, but it's still a rather high level (and successful) attempt to understand how these machines function.



>but to characterize our understanding of machine learning as not going beyond 3 or 4 neurons is just plain crazy.

There is a difference between understanding how something works and understanding why it works. Completely different levels of predictive power.


I'm sorry, lstms and convnets would seem to represent a rather high level of predictive power, given that someone postulated that they would work, and it turned out they were correct.




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