Reproduce “Differentiable Euler Characteristic Transforms for Shape Classification” on OpenResearch

About this paper

Ernst Roell, Bastian Rieck

Researchers at AIDOS Lab, Helmholtz Munich, developed the Differentiable Euler Characteristic Transform (DECT), a method making the Euler Characteristic Transform (ECT) differentiable and suitable for end-to-end deep learning. This approach enables deep neural networks to learn and leverage topological features for shape classification and optimization, demonstrating competitive performance with significantly improved computational efficiency across diverse data modalities.

Key insights

• Approximating the non-differentiable step in ECT with a sigmoid function allows for full differentiability, making complex topological features trainable within deep learning architectures.
• Learning optimal projection directions for the Euler Characteristic Transform yields improved classification accuracy and reduced variance compared to using fixed directions.
• DECT provides a computationally efficient and scalable method for incorporating topological information, achieving competitive performance on various shape classification tasks while being significantly faster than state-of-the-art graph neural networks.

Summary by alphaXiv.