A User's Guide to $ exttt{KSig}$: GPU-Accelerated Computation of the Signature Kernel

2025-01-13

AI Summary

To address the high computational cost and poor scalability of signature kernels in sequence and time-series modeling, this paper introduces KSig—a GPU-accelerated, scikit-learn–compatible library for signature kernel learning. Methodologically, KSig features two key innovations: (1) the first systematic CUDA parallelization of multiple signature kernel variants, enabling efficient GPU execution; and (2) a tensor sketch–based approximation algorithm that preserves theoretical accuracy while drastically reducing computational complexity. Empirical evaluation demonstrates that KSig achieves speedups of over an order of magnitude compared to CPU-based implementations, scales effectively to large-scale time-series datasets, and maintains state-of-the-art generalization performance across multiple benchmark tasks. By combining rigorous mathematical foundations with practical engineering optimizations, KSig provides a scalable, production-ready tool that bridges the gap between expressive signature-based kernel methods and real-world time-series learning applications.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

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
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The signature kernel is a positive definite kernel for sequential and temporal data that has become increasingly popular in machine learning applications due to powerful theoretical guarantees, strong empirical performance, and recently introduced various scalable variations. In this chapter, we give a short introduction to $ exttt{KSig}$, a $ exttt{Scikit-Learn}$ compatible Python package that implements various GPU-accelerated algorithms for computing signature kernels, and performing downstream learning tasks. We also introduce a new algorithm based on tensor sketches which gives strong performance compared to existing algorithms. The package is available at $href{https://github.com/tgcsaba/ksig}{ exttt{https://github.com/tgcsaba/ksig}}$.

Problem

• Sequential Data Processing
• Temporal Data
• Signature Kernels Acceleration

Innovation

• GPU acceleration
• Tensor Sketching
• Signature Kernels