CKConv: Continuous Kernel Convolution For Sequential Data
This work provides a novel convolutional approach for machine learning practitioners working with sequential and irregularly sampled data, offering a more efficient and effective alternative to existing methods.
The paper addresses limitations in recurrent and convolutional neural networks for sequential data by proposing Continuous Kernel Convolution (CKConv), which formulates CNN kernels as continuous functions. This approach enables modeling arbitrarily long sequences in parallel and achieves state-of-the-art results on datasets like permuted MNIST, while also handling non-uniformly and irregularly sampled data.
Conventional neural architectures for sequential data present important limitations. 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 their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.