加速拓扑特征计算，实现深度学习中的可微分处理。
Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorch
- GPU优化内核提升16-2000倍计算速度
- 支持端到端学习的可微分PyTorch层
- 适用于图像分析与深度学习场景
拓扑特征能捕捉成像数据中的全局几何结构，但其在深度学习中的实际应用需兼顾计算效率与可微性。本文提出针对欧拉特征曲线（ECC）计算的优化GPU内核，在合成网格上相较以往GPU实现提速16至2000倍，并引入一个可微分的PyTorch层，支持端到端学习。所设计的CUDA内核专为Ampere架构优化，采用128字节合并访问与分层共享内存累加。该PyTorch层通过类似可微欧拉特征变换的Sigmoid松弛，在单方向学习阈值。我们讨论了下游应用价值，涵盖先前ECC研究中强调的任务，并提出批处理与多GPU扩展方案以推动广泛应用。
原文摘要 · Abstract (English)
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.
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