Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorch
This work addresses the problem of integrating topological features into deep learning pipelines for researchers and practitioners in fields like imaging, by providing scalable and differentiable tools, though it is incremental in optimizing existing methods.
The paper tackles the computational inefficiency and lack of differentiability in using Euler Characteristic Curves for deep learning by developing optimized GPU kernels that achieve 16-2000x speedups over prior implementations and a differentiable PyTorch layer for end-to-end learning.
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 16-2000Ö 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.