Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Pad\'e Activation Units (PAUs) can both approximate common activation functions and also learn new ones while providing compact representations. Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance and reduce the training time of common deep architectures. Moreover, PAUs pave the way to approximations with provable robustness. The source code can be found at https://github.com/ml-research/pau