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Conventional neural architectures for sequential data present importantlimitations. Recurrent networks suffer from exploding and vanishing gradients,small effective memory horizons, and must be trained sequentially.Convolutional networks are unable to handle sequences of unknown size and theirmemory horizon must be defined a priori. In this work, we show that all theseproblems can be solved by formulating convolutional kernels in CNNs ascontinuous functions. The resulting Continuous Kernel Convolution (CKConv)allows us to model arbitrarily long sequences in a parallel manner, within asingle operation, and without relying on any form of recurrence. We show thatContinuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-artresults in multiple datasets, e.g., permuted MNIST, and, thanks to theircontinuous nature, are able to handle non-uniformly sampled datasets andirregularly-sampled data natively. CKCNNs match or perform better than neuralODEs designed for these purposes in a faster and simpler manner.

CKConv: Continuous Kernel Convolution For Sequential Data