I have a fair idea that a lot of research has been done and is still underway to explore the science behind the black art of a neural network (NN) architecture, i.e., accurately calculating the number of hidden layers and the number of neurons in each layer in an NN and we are yet to find a definite answer. I as part of my research developed a problem specific feedforward NN for binary classification (let's name it NN-1). The input data comprises of the 'Received Signal Strength' and/or 'Time of Flight' of the users transmitted signals recorded at static base stations. Now I am trying to defend the architecture of NN-1, i.e., that no other new NN architecture (which if designed with a different number of hidden layers and/or changed number of neurons in the hidden layer as compared to NN-1) can beat the performance (on test set) of NN-1. *Do note that training and the test sets for NN-1 and other NNs (with changed architecture) are the same. *
Few ideas I am considering are:
- To formulate a set of mathematical equations that helps in calculating/recommending an optimum number of hidden layers and the number of neurons in each layer for NN-1. It would work even if the derived mathematical equations are only valid for my specific classification problem. Once successful, I can modify NN-1's architecture accordingly and can confidently state NN-1 to have an optimum architecture. I would welcome if anyone can guide here or can point out to any related work (which has explored such mathematical approach towards determining the number of hidden layers/neurons in an NN) so that I can further capitalize on that. Please note that I have read a lot of literature during the past few months but have only come across guidelines on how to choose the number of hidden layers and the number of neurons in those layers.
- Independent of the above, I look forward to any ideas following which can help me in defending the NN-1's architecture.