🍩 Database of Original & Non-Theoretical Uses of Topology

1. Differentiable Euler Characteristic Transforms for Shape Classification (2023)

   Ernst Röell, Bastian Rieck

   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.

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   • Graph Classification
   • Graph Learning
   • Shape Classification
   • Graphs
   • Graphs:molecule
   • Innovate
   • Deep Learning
   • Euler Characteristic Transform
   • Machine Learning
   • Simplicial Complex