  Activation functions play a pivotal role in determining the training dynamics
and neural network performance. The widely adopted activation function ReLU
despite being simple and effective has few disadvantages including the Dying
ReLU problem. In order to tackle such problems, we propose a novel activation
function called Serf which is self-regularized and nonmonotonic in nature. Like
Mish, Serf also belongs to the Swish family of functions. Based on several
experiments on computer vision (image classification and object detection) and
natural language processing (machine translation, sentiment classification and
multimodal entailment) tasks with different state-of-the-art architectures, it
is observed that Serf vastly outperforms ReLU (baseline) and other activation
functions including both Swish and Mish, with a markedly bigger margin on
deeper architectures. Ablation studies further demonstrate that Serf based
architectures perform better than those of Swish and Mish in varying scenarios,
validating the effectiveness and compatibility of Serf with varying depth,
complexity, optimizers, learning rates, batch sizes, initializers and dropout
rates. Finally, we investigate the mathematical relation between Swish and
Serf, thereby showing the impact of preconditioner function ingrained in the
first derivative of Serf which provides a regularization effect making
gradients smoother and optimization faster.
