# How to mathematically define the architecture of neural network model? And the function space associated with it?

My goal is to properly define a search space for neural architecture search (NAS).

I think a proper definition must handle the following issues.

1. how to mathematically quantify the topology?
2. how to define the number in each layer? activation functions?
• Do you need the mathematical notion of how NN work? You may find them here – Shubham Panchal Apr 20 '19 at 2:11
• Besides the above reference, you can also look at the following: A. Pinkus,Approximation theory of the MLP model in neural networks, Acta Numerica (1999), pp. 143--195 (which provides a justification of why using Deep Neural Networks); and S. Shalev-Shwartz and S. Ben-David, Understanding machine learning: from theory to algorithms, Cambridge University Press, 2014. – Tuyen May 21 '19 at 4:15