THOI: Making Higher-Order Interaction Analysis Faster and Easier

What is it about?

THOI (Torch-based High-Order Interactions) is an open-source Python library for computing higher-order interactions (HOI) in continuous multivariate systems. The library was designed to make HOI analysis both computationally efficient and easy to integrate into real-world scientific workflows. THOI combines Gaussian-copula entropy estimation with modern batch-processing and parallelization strategies to accelerate computations across CPUs, GPUs, and TPUs. This allows users to efficiently compute higher-order information-theoretic measures that are traditionally expensive and difficult to scale. The project includes: * an installable Python package, * optimized implementations for large-scale analyses, * support for exhaustive and optimization-based HOI exploration, * and a collection of open tutorials reproducing the analyses from the paper as practical examples for new users. THOI is fully open source and openly available to the community, with all code, tutorials, and analysis pipelines publicly released to encourage reproducibility, reuse, and community contributions through issues and pull requests.

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Photo by Max Harlynking on Unsplash

Photo by Max Harlynking on Unsplash

Why is it important?

Many real-world systems cannot be fully understood by studying variables two at a time. Brain activity, ecosystems, financial markets, social dynamics, and biological systems all exhibit collective behaviors that emerge from interactions involving many components simultaneously. Higher-order interaction (HOI) analyses provide a way to study these collective effects, revealing patterns that remain invisible to standard pairwise approaches. Despite this potential, HOI methods have historically been underused because they are computationally demanding and difficult to scale. As the number of variables increases, the number of possible interactions grows explosively, often making analyses prohibitively slow or inaccessible for many researchers. THOI is important because it helps bridge this gap between theory and practice. By making HOI computations dramatically faster and easier to use, THOI allows researchers to incorporate higher-order analyses into everyday scientific workflows instead of treating them as niche or impractical methods. This opens the possibility of exploring collective dynamics at scales that were previously difficult to analyze, even on standard workstation hardware. In addition, THOI promotes reproducible and open science by providing open-source implementations, accessible tutorials, and reproducible analysis pipelines. We hope this lowers the barrier for researchers from different disciplines to explore higher-order interactions in their own data and contributes to broader adoption of HOI methods across science.

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