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I have a NN that I would like to square a number. This is a learning exercise for me.

My input is the number to be squared, the output is the square.

Two questions: 1) How can this possibly work? The weights and nodes of the NN need to square to a number that isn't fixed.

2) Assuming I am wrong, what is a strategy for choosing the numbers of nodes and layers for a NN?

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The ReLU activation function should take care of this.

ReLU works by fitting short, straight lines to approximate curves. That should be able to create a parabola. You will have performance suffer for inputs with very large absolute values, but we know that models won't be perfect.

I was thinking that one hidden layer could take care of this, but reading about the universal approximation theorem (which I suggest doing), we can be more efficient by having fewer nodes in multiple hidden layers than tons of nodes in one hidden layer.

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