How can I compare two different neural networks, from a theorical point of view? Let's say I have a problem (i.e. Given f(x), find x) and two neural networks(i.e. feedforward and recurrent). I would like to know if one works better than the other one. I could run the twos on a computer, but other programs might interfere and I wouldn't know if the implementations I'm running are really the best ones humankind could create. Moreover, how could I be sure that the feedforward network worked better than the recurrent, when it might have just been "lucky"?

So, here is the question: can I compare the efficiency of two neural networks(with known sizes, structures and functions) from a theorical point of view? And if the answer is yes, how?

Thank you in advance.
Essentially, no.  The only way to know which neural network is going to give you better accuracy is to try them on a realistic data set.  The theory we have is not well-enough developed to allow us to reliably predict which will do better on a particular data set.



A secondary remark.  When you remark "other programs might interfere", that's not correct.  Even if other programs are running (on a multi-tasking machine), they won't affect the accuracy.  They might take the process of running or training the neural network on your data set take longer, but they won't affect the results.