Differentiable Euler Characteristic Transforms for Shape Classification

Published: 16 Jan 2024, Last Modified: 19 Mar 2024ICLR 2024 posterEveryoneRevisionsBibTeX
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Keywords: Differentiable Euler Characteristic Transforms for Shape Classification
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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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Primary Area: learning on graphs and other geometries & topologies
Submission Number: 6202
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