A1171
Title: ECLayr: A fast and robust topological layer via Euler characteristic curves
Authors: Hajin Lee - Korea University (Korea, South) [presenting]
Jisu Kim - Seoul National University (Korea, South)
Kwangho Kim - Korea University (Korea, South)
Abstract: The purpose is to 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, the proposed method bypasses this bottleneck while retaining essential topological information across diverse data modalities. To enable complete end-to-end training, the authors develop a stable backpropagation scheme that mitigates vanishing gradient issues. A stability analysis is provided, demonstrating the robustness of the proposed layer against noise and outliers. The proposed layer is integrated into topological autoencoders to enhance representation learning through topological signals. The effectiveness of this approach is further demonstrated through classification experiments on a variety of datasets, including high-dimensional settings where persistent homology becomes computationally challenging.
