  In this work, we show that saturating output activation functions, such as
the softmax, impede learning on a number of standard classification tasks.
Moreover, we present results showing that the utility of softmax does not stem
from the normalization, as some have speculated. In fact, the normalization
makes things worse. Rather, the advantage is in the exponentiation of error
gradients. This exponential gradient boosting is shown to speed up convergence
and improve generalization. To this end, we demonstrate faster convergence and
better performance on diverse classification tasks: image classification using
CIFAR-10 and ImageNet, and semantic segmentation using PASCAL VOC 2012. In the
latter case, using the state-of-the-art neural network architecture, the model
converged 33% faster with our method (roughly two days of training less) than
with the standard softmax activation, and with a slightly better performance to
boot.
