I started to study and programming in neural networks for a little while now, but I never read about the minimum number of observations one must collect in a dataset to get robust results. Of course, more observations better results, but, Does exist an empirical or theoretical relationship between variables and observations number?

I mean, neither in econometrics you can compute the minimum number of observations, but it does exist some rule of thumbs that relies the number of exogenous variables to the target variable.

I wonder if there is something similar to that in neural networks too, but, till now, browsing on the internet, I did not find anything of useful.

Any ideas, advises or hint will be appreciated.