高效计算路径签名的GPU库，加速时序数据建模。
pathsig: A GPU-Accelerated Library for Truncated and Projected Path Signatures
- 直接在词基下用CUDA并行计算签名系数
- 计算截断签名快10-30倍，训练快4-10倍
- 支持自定义词集投影与非均匀截断，降低冗余
路径签名能为序列数据提供丰富表征，具备强理论保障且在多种机器学习任务中表现良好。尽管签名已从固定特征提取器演变为可训练组件，但现有库在大规模梯度学习下的可扩展性不足。为此，本文提出 pathsig，一个原生 PyTorch 的库，直接在词基下计算路径签名。通过使用 CUDA 内核在前缀闭包词集上并行更新签名系数，pathsig 实现高 GPU 吞吐量和近最小峰值内存。相比其他库，pathsig 在截断签名计算上提速 10–30 倍，在需反向传播的训练中提速达 4–10 倍。除常规截断外，pathsig 支持将（无限维）签名投影至用户指定词集，并实现基于路径异质正则性的各向异性截断，从而生成更紧凑表征，降低维度、冗余与计算开销。
原文摘要 · Abstract (English)
Path signatures provide a rich representation of sequential data, with strong theoretical guarantees and good performance in a variety of machine-learning tasks. While signatures have progressed from fixed feature extractors to trainable components of machine-learning models, existing libraries often lack the required scalability for large-scale, gradient-based learning. To address this gap, this paper introduces pathsig, a PyTorch-native library that computes path signatures directly in the word basis. By using CUDA kernels to update signature coefficients in parallel over prefix-closed word sets, pathsig achieves high GPU throughput and near-minimal peak memory. Compared with other libraries, pathsig achieves 10-30x speedups for computation of truncated signatures and up to 4-10x speedups in training that require backpropagation through the signature. Beyond regular truncation, pathsig supports projections of the (infinite-dimensional) signature onto user-specified sets of words and anisotropic truncation motivated by inhomogeneous path regularity, enabling more compact representations that can reduce dimensionality, redundancy, and computational cost.
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