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Convolutional neural networks (CNNs) have become the state-of-the-art toolfor dealing with unsolved problems in computer vision and image processing.Since the convolution operator is a linear operator, several generalizationshave been proposed to improve the performance of CNNs. One way to increase thecapability of the convolution operator is by applying activation functions onthe inner product operator. In this paper, we will introduce PowerLinearactivation functions, which are based on the polynomial kernel generalizationof the convolution operator. EvenPowLin functions are the main branch of thePowerLinear activation functions. This class of activation functions issaturated neither in the positive input region nor in the negative one. Also,the negative inputs are activated with the same magnitude as the positiveinputs. These features made the EvenPowLin activation functions able to beutilized in the first layer of CNN architectures and learn complex features ofinput images. Additionally, EvenPowLin activation functions are used in CNNmodels to classify the inversion of grayscale images as accurately as theoriginal grayscale images, which is significantly better than commonly usedactivation functions.

PowerLinear Activation Functions with application to the first layer of CNNs