Fractional Adaptation of Activation Functions In Neural Networks

In this work, we introduce a generalization methodology for the automatic selection of the activation functions inside a neural network, taking advantage of concepts defined in fractional calculus. This methodology enables the neural network to search and optimize its own activation functions during the training process, by defining the fractional order of the derivative of a given primitive activation function. This fractional order is tuned as an additional training hyper-parameter $a$ for intrafamily selection and $b$ for cross family selection. By following this approach, the neurons inside the network can adjust their activation functions, e.g. from MLP to RBF networks, to best fit the input data, and reduce the output error. The experimental results obtained show the benefits of using this technique implemented on a ResNet18 topology, by outperforming the accuracy of a ResNet100 trained with CIFAR10 and Improving 1% ImageNet reported in the literature.