  Many neural network architectures rely on the choice of the activation
function for each hidden layer. Given the activation function, the neural
network is trained over the bias and the weight parameters. The bias catches
the center of the activation, and the weights capture the scale. Here we
propose to train the network over a shape parameter as well. This view allows
each neuron to tune its own activation function and adapt the neuron curvature
towards a better prediction. This modification only adds one further equation
to the back-propagation for each neuron. Re-formalizing activation functions as
CDF generalizes the class of activation function extensively. We aimed at
generalizing an extensive class of activation functions to study: i) skewness
and ii) smoothness of activation functions. Here we introduce adaptive Gumbel
activation function as a bridge between Gumbel and sigmoid. A similar approach
is used to invent a smooth version of ReLU. Our comparison with common
activation functions suggests different data representation especially in early
neural network layers. This adaptation also provides prediction improvement.

Machine Learning;Machine Learning