DECT - Differentiable Euler Characteristic Transform

This is the official repository for the ICLR 2024 paper: Differentiable Euler Characteristic Transforms for Shape Classification.

Abstract The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method, the Differentiable Euler Characteristic Transform (DECT), is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly simple statistic provides the same topological expressivity as more complex topological deep learning layers.

Please use the following citation for our work:

@inproceedings{Roell24a,
  title         = {Differentiable Euler Characteristic Transforms for Shape Classification},
  author        = {Ernst R{\"o}ell and Bastian Rieck},
  year          = 2024,
  booktitle     = {International Conference on Learning Representations},
  eprint        = {2310.07630},
  archiveprefix = {arXiv},
  primaryclass  = {cs.LG},
  repository    = {https://github.com/aidos-lab/DECT},
  url           = {https://openreview.net/forum?id=MO632iPq3I},
}

Installation

Our code has been developed using python 3.10 and using pytorch 2.0.1 installed with CUDA 11.7. After installing the above, install the requirements in the requirements.txt.

pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu117
pip install -r requirements.txt

Usage

To run a single experiment, run single_main.py and modify the path to the right experiment. The configuration files for each experiment can be found under the experiment folder and the parameters are in the .yaml files.

To run all experiments in a folder, update the path in main.py to that folder and run main.py.

All datasets will be downloaded and preprocessed when first ran via the torch_geometric package. The TU Datasets are small and run fast, so for testing purposes it is recommended to run these first.

Alternatively, for research purposes the ECT is installable as a python package. To install DECT, run the following in the terminal

pip install "git+https://github.com/aidos-lab/DECT/#subdirectory=dect"

For example usage, we provide the example.ipynb file and the code therein reproduces the ECT of the gif of this readme. The code is provided on an as is basis. You are cordially invited to both contribute and provide feedback. Do not hesitate to contact us.

Examples

The core of our method, the differentiable computation of the Euler Characteristic transform, can be found in the ./models/layers/layers.py folder. Since the code is somewhat terse, highly vectorised and optimized for batch processing, we provide an example computation that illustrates the core principle of our method.

License

Our code is released under a BSD-3-Clause license. This license essentially permits you to freely use our code as desired, integrate it into your projects, and much more --- provided you acknowledge the original authors. Please refer to LICENSE.md for more information.

Issues

This project is maintained by members of the AIDOS Lab. Please open an issue in case you encounter any problems.