Differentiable Euler Characteristic Transforms for Shape Classification
This work addresses the limitation of non-learnable topological representations in shape classification, offering a computationally efficient alternative to complex topological deep learning layers.
The paper tackled the problem of making the Euler Characteristic Transform (ECT) learnable for task-specific shape representations, resulting in the Differentiable Euler Characteristic Transform (DECT) that achieves performance comparable to more complex models in graph and point cloud classification tasks.
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, 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.