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

arXiv: https://arxiv.org/abs/2510.20271 · HTML: https://mlsanity.com/paper/2510.20271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 6 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 2 of 2)

- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)

## Built on by (most cited first, 1 of 1)

- [Tensor Computation of Euler Characteristic Functions and Transforms](https://mlsanity.com/paper/2511.03909/) (2025)

## Abstract (arXiv)

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.