  Performant Convolutional Neural Network (CNN) architectures must be tailored
to specific tasks in order to consider the length, resolution, and
dimensionality of the input data. In this work, we tackle the need for
problem-specific CNN architectures. We present the Continuous Convolutional
Neural Network (CCNN): a single CNN able to process data of arbitrary
resolution, dimensionality and length without any structural changes. Its key
component are its continuous convolutional kernels which model long-range
dependencies at every layer, and thus remove the need of current CNN
architectures for task-dependent downsampling and depths. We showcase the
generality of our method by using the same architecture for tasks on sequential
($1{\rm D}$), visual ($2{\rm D}$) and point-cloud ($3{\rm D}$) data. Our CCNN
matches and often outperforms the current state-of-the-art across all tasks
considered.
