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.

翻译：卷积神经网络（CNN）是深度学习中最核心的架构之一。CNN的基本构建模块是表示为离散网格的可训练滤波器，用于对离散输入数据进行卷积运算。本文提出了一种连续版本的可训练卷积滤波器，使其同样能够处理非结构化数据。这一新框架使卷积神经网络能够突破离散域的局限，将该重要学习技术的应用范围拓展至更多复杂问题。实验表明，该连续滤波器能够达到与当前最先进离散滤波器相当的精度水平，并可作为基础模块融入现有深度学习架构，有效解决非结构域问题。