A Continuous Convolutional Trainable Filter for Modelling Unstructured Data

In the deep learning field, a convolutional neural network (CNN) [28] is one of the most important architectures, widely used in academia and industrial research. For an overview of the topic, the interested reader might refer to [30, 16, 2, 5, 52]. Despite the great success in many fields including, but not limited, to computer vision [26, 40, 22] or natural language processing [50, 11], current CNNs are constrained to structural data. Indeed, the basic building block of a CNN is a trainable filter, represented by a discrete grid, which performs cross-correlation, also known as convolution, on a discrete domain. Nevertheless, the idea behind convolution can be easily extended mathematically to unstructured domains, for reference see [18]. One possible approach for this kind of problem is the graph neural networks (GNN) [24, 49], where a graph is built starting from the topology of the discretized space.