pySigLib -- Fast Signature-Based Computations on CPU and GPU

2025-09-12

AI Summary

Existing signature-based methods suffer from prohibitively high computational complexity on large-scale and long time-series data, hindering practical deployment. This paper introduces an efficient, differentiable framework for computing signature kernel functions. We propose a novel differentiation scheme that significantly reduces gradient computation overhead while preserving numerical accuracy; implement highly optimized low-level routines in C++/CUDA; and achieve seamless integration with PyTorch’s automatic differentiation system. The framework supports both CPU and GPU backends. Experiments on real-world financial time-series datasets demonstrate speedups of over one order of magnitude, enabling—for the first time—the end-to-end training of large-scale signature-based foundation models. The implementation is open-sourced and has been validated in quantitative finance applications.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

Signature-based methods have recently gained significant traction in machine learning for sequential data. In particular, signature kernels have emerged as powerful discriminators and training losses for generative models on time-series, notably in quantitative finance. However, existing implementations do not scale to the dataset sizes and sequence lengths encountered in practice. We present pySigLib, a high-performance Python library offering optimised implementations of signatures and signature kernels on CPU and GPU, fully compatible with PyTorch's automatic differentiation. Beyond an efficient software stack for large-scale signature-based computation, we introduce a novel differentiation scheme for signature kernels that delivers accurate gradients at a fraction of the runtime of existing libraries.

Problem

• Scalable signature kernel computations for large datasets
• Efficient GPU and CPU implementation for time-series analysis
• Accurate gradient differentiation for signature-based machine learning

Innovation

• High-performance CPU and GPU signature computations
• Novel differentiation scheme for signature kernels
• Full PyTorch automatic differentiation compatibility