In neural networks model, which number of hidden units to select?
Unfrtunately not, there is not theory to tell us what is the right number of units to choose. As there is not theory for the number of hidden layers to choose. On this respect, Deep Learning is still more an art than a science.

It's true that with one hidden layer we could theoretically solve any problem, but most of the problems are complicated enough to require unimaginable amounts computation.

I think in the end it all boils down to two main issues:


Your specific task, i.e. how large and deep a Network must be so that your model works as you need.
The compute power at your disposal.


When it comes to this, I strongly suggest to prioritize depth over width. Deeper Networks (the ones with many hidden layers) are much more efficient and powerful than large Networks (the ones with fewer, larger layers). It seems they are better at producing abstractions on the input data, to transform and process the signal in more sophisticated ways.