  Deep networks are gradually penetrating almost every domain in our lives due
to their amazing success. However, with substantive performance accuracy
improvements comes the price of \emph{irreproducibility}. Two identical models,
trained on the exact same training dataset may exhibit large differences in
predictions on individual examples even when average accuracy is similar,
especially when trained on highly distributed parallel systems. The popular
Rectified Linear Unit (ReLU) activation has been key to recent success of deep
networks. We demonstrate, however, that ReLU is also a catalyzer to
irreproducibility in deep networks. We show that not only can activations
smoother than ReLU provide better accuracy, but they can also provide better
accuracy-reproducibility tradeoffs. We propose a new family of activations;
Smooth ReLU (\emph{SmeLU}), designed to give such better tradeoffs, while also
keeping the mathematical expression simple, and thus implementation cheap.
SmeLU is monotonic, mimics ReLU, while providing continuous gradients, yielding
better reproducibility. We generalize SmeLU to give even more flexibility and
then demonstrate that SmeLU and its generalized form are special cases of a
more general methodology of REctified Smooth Continuous Unit (RESCU)
activations. Empirical results demonstrate the superior
accuracy-reproducibility tradeoffs with smooth activations, SmeLU in
particular.
