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Neural networks are also called as the universal function approximation which is based in the universal function approximation theorem. It states that:

In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function

Meaning a ANN with a non linear activation function could map the function which relates the input with the output. The function $y = x^2$ could be easily approximated using regression ANN.

You can find an excellent lesson here with a notebook example.

Also, because of such ability ANN could map complex relationships for example between an image and its labels.

Neural networks are also called as the universal function approximation which is based in the universal function approximation theorem. It states that:

In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function

Meaning a ANN with a non linear activation function could map the function which relates the input with the output. The function $y = x^2$ could be easily approximated using regression ANN.

You can find an excellent lesson here with a notebook example. And there is a great visual proof that neural networks can compute any function.

Also, because of such ability ANN could map complex relationships for example between an image and its labels.

Neural networks are also called as the universal function approximation which is based in the universal function approximation theorem. It states that:

In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function

Meaning a ANN with a non linear activation function could map the function which relates the input with the output. The function y = x$^2$ could be easily approximated using regression ANN.

You can find an excellent lesson here with a notebook example.

Also, because of such ability ANN could map complex relationships for example between an image and its labels.

Neural networks are also called as the universal function approximation which is based in the universal function approximation theorem. It states that:

In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function

Meaning a ANN with a non linear activation function could map the function which relates the input with the output. The function $y = x^2$ could be easily approximated using regression ANN.

You can find an excellent lesson here with a notebook example.

Also, because of such ability ANN could map complex relationships for example between an image and its labels.

Neural networks are also called as the universal function approximation which is based in the universal function approximation theorem. It states that  :

In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function

Meaning a ANN with a non linear activation function could map the function which relates the input with the output. The function y = x^2 could be easily approximated using regression ANN.

You can find an excellent lesson here with a notebook example.

Also, because of such ability ANN could map complex relationships for example between an image and its labels.

Neural networks are also called as the universal function approximation which is based in the universal function approximation theorem. It states that:

In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function

Meaning a ANN with a non linear activation function could map the function which relates the input with the output. The function y = x$^2$ could be easily approximated using regression ANN.

You can find an excellent lesson here with a notebook example.

Also, because of such ability ANN could map complex relationships for example between an image and its labels.