  The use of Convolutional Neural Networks (CNNs) is widespread in Deep
Learning due to a range of desirable model properties which result in an
efficient and effective machine learning framework. However, performant CNN
architectures must be tailored to specific tasks in order to incorporate
considerations such as the input length, resolution, and dimentionality. In
this work, we overcome the need for problem-specific CNN architectures with our
Continuous Convolutional Neural Network (CCNN): a single CNN architecture
equipped with continuous convolutional kernels that can be used for tasks on
data of arbitrary resolution, dimensionality and length without structural
changes. Continuous convolutional kernels model long range dependencies at
every layer, and remove the need for downsampling layers and task-dependent
depths needed in current CNN architectures. We show the generality of our
approach by applying the same CCNN to a wide set of tasks on sequential
(1$\mathrm{D}$) and visual data (2$\mathrm{D}$). Our CCNN performs
competitively and often outperforms the current state-of-the-art across all
tasks considered.
