ECLayr: A Fast and Robust Topological Layer via Euler Characteristic Curves

TMLR Paper7391 Authors

Abstract: We introduce a flexible and computationally efficient topological layer for general deep learning architectures, built upon the Euler Characteristic Curve. Unlike existing approaches that rely on computationally intensive persistent homology, our method bypasses this bottleneck while retaining essential topological information across diverse data modalities. To enable complete end-to-end training, we develop a novel backpropagation scheme that improves computation and mitigates vanishing gradient issues. We go on to provide stability analysis, establishing stability guarantees for the proposed layer in the presence of noise and outliers. We integrate the proposed layer into topological autoencoders to enhance representation learning through topological signals. We further demonstrate the effectiveness of our approach through classification experiments on a variety of datasets, including high-dimensional settings where persistent homology becomes computationally challenging.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Fuxin_Li1

Submission Number: 7391