# Tradeoff between running time and depth in neural network

I might not be in the good stack-exchange site, so please forgive me.

Let consider a neural network that we want to train to a certain task. For the purpose of my research, I am wiling to reduce the number of operations during the training process within my encrypted neural network (homomorphically encrypted). However, I'm definitely not an expert in this domain and I would need some insights.

The weights inside my neural network are all encrypted in a way that allows normal computations (and hence proper training phase). However, encrypted operations are much more costly than operations on clear data.

Practically, if we want to reach a certain value for the error function (let's say $$E < 0.01$$) for instance, does there exist a tradeoff between number of operations and depth of the neural network.

As far as I know, people tend to find the accurate size of a neural network by trials and intuition but maybe some people made some theoretical results on this kind of tradeoff (even for only one specific kind of NN) ? If you have any paper to recommend I would gladly take them!

• why the downvote? – vidyarthi Apr 10 '19 at 10:09