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 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 unexpressive statistic still provides the same topological expressivity as more complex topological deep learning layers provide.

翻译：欧拉示性数变换已被证明是一种强大表示方法，能够结合形状和图结构的几何与拓扑特征。然而，该变换此前无法学习任务特定表示。我们解决了这一问题，开发出新型计算层，使欧拉示性数变换能够以端到端方式学习。我们的DECT方法快速且计算高效，在图分类和点云分类任务中均表现出与更复杂模型相当的性能。此外，我们证明这种看似缺乏表达力的统计量，实际上能提供与更复杂的拓扑深度学习层相同的拓扑表达力。