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This repository contains the source code accompanying the paper:

CKConv: Continuous Kernel Convolution For Sequential Data [Slides] [Demos]
David W. Romero, Anna Kuzina, Erik J. Bekkers, Jakub M. Tomczak & Mark Hoogendoorn.

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 at least match neural ODEs designed for these purposes in a much faster and simple manner.

This repository is organized as follows:

• ckconv contains the main PyTorch library of our model.

• datasets implements Dataset wrappers for the datasets used.

• ckernel_fitting contains source code to run experiments to approximate convolutional filters via MLPs. Please see ckernel_fitting/README.md for further details.

• demo provides some minimalistic examples on the usage of CKConvs and the construction of CKCNNs.

• models contains the models used throughout our experiments.

• probspec_routines contains routines specific to some of the problems considered in this paper.

• runs contains the command lines used to obtain the results reported in our experiments.

• saved contains various pretrained models.

In order to reproduce our results, please first install the required dependencies. This can be done by:

conda env create -f conda_requirements.txt

This will create the conda environment ckconv with the correct dependencies.

The same conda environment can be created with pip by running:

conda create -n ckconv python=3.7
conda activate ckconv
conda install pytorch==1.7.0 torchvision==0.8.1 torchaudio=0.7.0 cudatoolkit=10.1 -c pytorch
pip install -r requirements.txt

If you prefer to construct the conda environment manually, please follow the commands speficiend in manual_installation.txt

To reproduce the experiments in the paper, please follow the configurations given in runs/README.md

Specifications on the parameters specified via the argsparser can be found in the corresponding config.py file.

To use pretrained models, please add the argument --config.pretrained=True to the corresponding execution line.

We leverage the convolution theorem in our experiments to accelerate the computation of the convolution operations (see causal_fftconv in ckconv/nn/functional/causalconv.py), and we strongly recommend using fft convolutions. However, for some applications it might be desirable to rely on spatial convolutions, e.g., small conv. kernels. This can be easily modified by replacing the call to causal_fftconv in the forward pass of the CKConv class (ckconv/nn/ckconv.py:182) by the function causal_conv found in ckconv/nn/functional/causalconv.py.

If you found this work useful in your research, please consider citing:

@article{romero2021ckconv,
  title={CKConv: Continuous Kernel Convolutions for Sequential Data},
  author={Romero, David W and Kuzinna, Anna and Bekkers, Erik J and Tomczak, Jakub M and Hoogendoorn, Mark},
  journal={arXiv preprint arXiv:2102.02611},
  year={2021}
}

We gratefully acknowledge Gabriel Dernbach for interesting analyses on the knot distribution of ReLU networks. We thank Emiel van Krieken and Ali el Hasouni as well for interesting questions and motivating comments at the beginning of this project. David W. Romero is financed as part of the Efficient Deep Learning (EDL) programme (grant number P16-25), partly funded by the Dutch Research Council (NWO) and Semiotic Labs. Anna Kuzina is funded by the Hybrid Intelligence Center, a 10-year programme funded by the Dutch Ministry of Education, Culture and Science through the Netherlands Organisation for Scientific Research. Erik J. Bekkers is financed by the research programme VENI (grant number 17290) funded by the Dutch Research Council. All authors are thankful to everyone involved in funding this work. This work was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative.