pathsig: A GPU-Accelerated Library for Truncated and Projected Path Signatures

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.