Fractional Adaptive Linear Units

This work introduces Fractional Adaptive Linear Units (FALUs), a flexible generalization of adaptive activation functions. Leveraging principles from fractional calculus, FALUs define a diverse family of activation functions (AFs) that encompass many traditional and state-of-the-art activation functions. This family includes the Sigmoid, Gaussian, ReLU, GELU, and Swish functions, as well as a large variety of smooth interpolations between these functions. Our technique requires only a small number of additional trainable parameters, and needs no further specialized optimization or initialization procedures. For this reason, FALUs present a seamless and rich automated solution to the problem of activation function optimization. Through experiments on a variety of conventional tasks and network architectures, we demonstrate the effectiveness of FALUs when compared to traditional and state-of-the-art AFs. To facilitate practical use of this work, we plan to make our code publicly available.