Back-of-the-envelope machine learning (specifically neural networks) calculations There is a popular story regarding the back-of-the-envelope calculation performed by a British physicist named G. I. Taylor. He used dimensional analysis to estimate the power released by the explosion of a nuclear bomb, simply by analyzing a picture that was released in a magazine at the time.

I believe many of you know some nice back-of-the-envelope calculations performed in machine learning (more specifically neural networks). Can you please share them?
I have one to share. This is no formula, but a general thing I have noticed. 

The number of neurons + neurons should be proportionate, in some way, to the complexity of the classification.

Although this is fairly basic and widely known, it has helped me in many times to consider one thing: how many at a minimum does it need?