  Convolutional Neural Network (CNN) is one of the most important architectures
in deep learning. The fundamental building block of a CNN is a trainable
filter, represented as a discrete grid, used to perform convolution on discrete
input data. In this work, we propose a continuous version of a trainable
convolutional filter able to work also with unstructured data. This new
framework allows exploring CNNs beyond discrete domains, enlarging the usage of
this important learning technique for many more complex problems. Our
experiments show that the continuous filter can achieve a level of accuracy
comparable to the state-of-the-art discrete filter, and that it can be used in
current deep learning architectures as a building block to solve problems with
unstructured domains as well.
