Artificial Intelligence (AI) Development

Is there a mathematical theory behind why MLP can classify hand written digits?

I’m trying to really understand how multi-layer perceptrons works. I want to prove mathematically that MLP’s can classify hand written 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 back prop 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.

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