  In this paper, we propose a fixed convolutional layer with an order of
smoothness not only for avoiding checkerboard artifacts in convolutional neural
networks (CNNs) but also for enhancing the performance of CNNs, where the
smoothness of its filter kernel can be controlled by a parameter. It is
well-known that a number of CNNs generate checkerboard artifacts in both of two
process: forward-propagation of upsampling layers and backward-propagation of
strided convolutional layers. The proposed layer can perfectly prevent
checkerboard artifacts caused by strided convolutional layers or upsampling
layers including transposed convolutional layers. In an image-classification
experiment with four CNNs: a simple CNN, VGG8, ResNet-18, and ResNet-101,
applying the fixed layers to these CNNs is shown to improve the classification
performance of all CNNs. In addition, the fixed layer are applied to generative
adversarial networks (GANs), for the first time. From image-generation results,
a smoother fixed convolutional layer is demonstrated to enable us to improve
the quality of images generated with GANs.
