Differentiable Euler Characteristic Transforms for Shape Classification

Ernst Röell, Bastian Rieck

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: Differentiable Euler Characteristic Transforms for Shape Classification

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

Abstract:

The _Euler Characteristic Transform_ (ECT) is a powerful
invariant, 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.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 6202