rationale behind multi-layer networks

Question

I recently read that a feed forward neural network with a single hidden layer can represent any continuous function to great precision (ref.). Then how can we justify adding more that one hidden layer to our network ?

Answer 1

The rationale is that the number of neurones you need to use for approximating any given contiguous function decreases as you add subsequent layers. See Colah's Deep Learning, NLP, and Representations for a more in-depth explanation.