QCNN: Quadrature Convolutional Neural Network with Application to Unstructured Data Compression

We present a new convolution layer for deep learning architectures which we call QuadConv -- an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on unstructured data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. In the setting of neural compression, we show that a QuadConv-based autoencoder, resulting in a Quadrature Convolutional Neural Network (QCNN), can match the performance of standard discrete convolutions on structured uniform data, as in CNNs, and maintain this accuracy on unstructured data.