Parabolic integrodifferential splines as activation functions to increase the efficiency of information processing by neural networks

The paper considers the method to increase the efficiency of information processing by neural networks by using the parabolic integrodifferential splines (ID-splines) developed by the author as an activation function (AF) for neurons. If the coefficients of parabolic ID-splines along with the weights of the neurons are the trainable parameters of the neural network, then the AF in the form of a parabolic ID spline changes in the learning process to minimize the error function. This increases the accuracy of the results of the neural network calculations and accelerates its training and operation. The prospects for modifying neural networks with known architectures (such as ResNet) by introducing ID-spline as AF are analyzed. Apparently, such an approach can improve the quality of functioning of some popular neural networks. It is concluded that parabolic ID splines as AF can increase the efficiency of artificial intelligence technologies in such tasks as decision making, computer games development, approximating and predicting data (in the financial and social spheres, in science, etc.), classification of information, processing of images and videos, application of computer vision, processing of texts, speech, and music, etc.