Differentiable Euler Characteristic Transforms for Shape Classification
Authors: Ernst Röell,Bastian Rieck
Presentation: ICLR 2024,Poster

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.