Smooth activations and reproducibility in deep networks

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 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 (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. Recent developments in deep learning leave no question about the advantages of deep networks over classical methods, which relied heavily on linear convex optimization solutions. With their astonishing unprecedented success, deep models are providing solutions to a continuously increasing number of domains in our lives. These solutions, however, while much more accurate than their convex counterparts, are usually irreproducible in the predictions they provide. While average accuracy of deep models on some validation dataset is usually much higher than that of linear convex models, predictions on individual examples of two models, that were trained to be identical, may diverge substantially, exhibiting Prediction Differences that may be as high as non-negligible fractions of the actual predictions (see, e.g., Chen et al. (2020); Dusenberry et al. (2020)). Deep networks express (only) what they learned.