Convolutional Filter Approximation Using Fractional Calculus

Abstract

We introduce a generalized fractional convolutional filter (FF) with the flexibility to behave as any novel, customized, or well-known filter (e.g. Gaussian, Sobel, and Laplacian). Our method can be trained using only five parameters – regardless of the kernel size. Furthermore, these kernels can be used in place of traditional kernels in any CNN topology. We demonstrate a nominal 5X parameter compression per kernel as compared to a traditional (5 × 5) convolutional kernel, and in the generalized case, a compression from N × N to 6 trainable parameters per kernel. We furthermore achieve 43X compression for 3D convolutional filters compared with conventional (7 × 7 × 7) 3D filters. Using fractional filters, we set a new MNIST record for the fewest number of parameters required to achieve above 99% classification accuracy with only 3, 750 trainable parameters. In addition to providing a generalizable method for CNN model compression, FFs present a compelling use case for the compression of CNNs that require large kernel sizes (e.g. medical imaging, semantic segmentation).