Universality Theorem
Neural networks with a single hidden layer can be used to approximate any continuous function to any desired precision.
Problems
Universality means that, in principle, neural networks can do all these things and many more. However, the appropriate neural network for a certain problem is not easy to find. Just because we know a neural network exists that can translate Chinese text into English, that doesn't mean we have good techniques for constructing or even recognizing such a network.
