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In some sense, you're right that a neural net is just another tool to fit data. However, it's quite the tool! There's this universal approximation theorem saying that, under decent conditions, a neural network can get as close as you want to a wide class of functions. This means that you can get the network to give you complicated shapes with squiggles all ...

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neural networks can solve all taylor series polynomials meaning a NN is an generalized linear model. Most function f(y) can be solved with neural networks. However, many matrix operations can not be generalized for a neural network to solve like determinants. Operations like rotation, scale, and transform also can not be generalized. you can solve all ...

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It is indeed true that neural networks are just another ways of curve fitting. In fact, as I learned regression after I learned neural networks, I shout out "neural networks are just more sophisticated curve fitting!". However, as Dave said, it can approximate any function in practice. See Google's neural net playground for an interesting animation....

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