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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
PubMed
Summary
This summary is machine-generated.

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.

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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.