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THOI: An efficient and accessible library for computing higher-order interactions enhanced by batch-processing
Laouen Belloli1,2,3, Pedro A M Mediano4,5, Rodrigo Cofré6
1Laboratorio de Inteligencia Artificial Aplicada, Instituto de Ciencias de la Computación, Universidad de Buenos Aires, Buenos Aires, Argentina.
Plos One
|May 11, 2026
Summary
This study introduces THOI, a Python library for analyzing complex systems by quantifying higher-order interactions. THOI efficiently estimates joint entropies, enabling deeper insights into nonlinear dynamics and emergent behaviors.
Area of Science:
- Complex Systems Science
- Information Theory
- Computational Neuroscience
Background:
- Complex systems exhibit nonlinear dynamics and emergent behaviors driven by higher-order interactions.
- Traditional analyses often overlook these higher-order interactions, leading to oversimplified models.
- Multivariate information theory offers tools to quantify higher-order interactions, but faces challenges in entropy estimation and computational complexity.
Purpose of the Study:
- Introduce THOI (Torch-based High-Order Interactions), a novel Python library for efficient computation of higher-order interactions in continuous-valued complex systems.
- Address the persistent challenges of accurate joint entropy estimation and the combinatorial explosion of interacting terms in multivariate analysis.
- Provide a scalable and accessible tool for researchers to analyze the multi-level, nonlinear, and multidimensional nature of complex systems.
Main Methods:
- Leveraged the Gaussian copula method for robust joint entropy estimation in continuous data.
- Implemented state-of-the-art batch and parallel processing techniques for optimized performance across CPU, GPU, and TPU.
- Integrated optimization strategies to make higher-order interaction analysis feasible for large-scale systems where exhaustive analysis is impractical.
Main Results:
- THOI significantly outperforms existing tools in speed and scalability for analyzing higher-order interactions.
- Demonstrated substantial reductions in computation time for exhaustive analysis of small systems (≤ 30 variables).
- Validated THOI's accuracy using synthetic datasets and demonstrated its utility in analyzing real-world fMRI data.
Conclusions:
- THOI provides an efficient, scalable, and accessible framework for higher-order interaction (HOI) analysis in complex systems.
- The library facilitates the testing of hypotheses regarding the nonlinear and multidimensional characteristics of complex systems.
- THOI opens new avenues for understanding emergent collective behaviors and multi-level interactions across diverse scientific domains.
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