Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorch

TL;DR

This paper introduces highly optimized GPU kernels for computing Euler Characteristic Curves, significantly speeding up the process, and presents a differentiable PyTorch layer for end-to-end learning in deep neural networks.

Contribution

The work provides the first GPU-accelerated, differentiable implementation of ECC computation, enabling efficient topological feature learning within deep learning frameworks.

Findings

Achieved 16-2000x speedups over previous GPU implementations.

Developed a differentiable PyTorch layer for ECC-based threshold learning.

Outlined batching and multi-GPU extensions for broader applicability.

Abstract

Topological features capture global geometric structure in imaging data, but practical adoption in deep learning requires both computational efficiency and differentiability. We present optimized GPU kernels for the Euler Characteristic Curve (ECC) computation achieving 16-2000\"O speedups over prior GPU implementations on synthetic grids, and introduce a differentiable PyTorch layer enabling end-to-end learning. Our CUDA kernels, optimized for Ampere GPUs use 128B-coalesced access and hierarchical shared-memory accumulation. Our PyTorch layer learns thresholds in a single direction via a Differentiable Euler Characteristic Transform-style sigmoid relaxation. We discuss downstream relevance, including applications highlighted by prior ECC work, and outline batching/multi-GPU extensions to broaden adoption.