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The choice of activation function can significantly influence the performanceof neural networks. The lack of guiding principles for the selection ofactivation function is lamentable. We try to address this issue by introducingour variational neural networks, where the activation function is representedas a linear combination of possible candidate functions, and an optimalactivation is obtained via minimization of a loss function using gradientdescent method. The gradient formulae for the loss function with respect tothese expansion coefficients are central for the implementation of gradientdescent algorithm, and here we derive these gradient formulae.

Variational Neural Networks: Every Layer and Neuron Can Be Unique