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Performant Convolutional Neural Network (CNN) architectures must be tailoredto specific tasks in order to consider the length, resolution, anddimensionality of the input data. In this work, we tackle the need forproblem-specific CNN architectures. We present the Continuous ConvolutionalNeural Network (CCNN): a single CNN able to process data of arbitraryresolution, dimensionality and length without any structural changes. Its keycomponent are its continuous convolutional kernels which model long-rangedependencies at every layer, and thus remove the need of current CNNarchitectures for task-dependent downsampling and depths. We showcase thegenerality 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 CCNNmatches and often outperforms the current state-of-the-art across all tasksconsidered.

Modelling Long Range Dependencies in $N$D: From Task-Specific to a General Purpose CNN