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I'm trying to really understand how multi-layer perceptrons work. I want to prove mathematically that MLP's can classify handwritten digits. The only thing I really have is that each perceptron can operate exactly like a logical operand, which obviously can classify things, and, with backpropagation and linear classification, it's obvious that, if a certain pattern exists, it'll activate the correct gates in order to classify correctly, but that is not a mathematical proof.

This is probably a special case of the universal approximation theorem. Here is a Wikipedia page about the theorem.

– senderle – 2020-02-14T23:51:27.673