Scalable detection of higher-order interactions in network data

2026-09-27

AI Summary

This study addresses the challenge of efficiently recovering latent higher-order hypergraph structures from pairwise network data while overcoming the scalability bottlenecks of existing methods. To this end, this work reformulates hypergraph reconstruction as a local signal-to-noise ratio discrimination problem. By integrating local signal processing with hypergraph theory and information-theoretic analysis, it derives an information-theoretic detectability threshold that enables the rapid reconstruction of interactions of arbitrary order. The proposed algorithm accurately recovers latent higher-order structures across diverse complex systems, achieving computational speeds several orders of magnitude faster than state-of-the-art approaches. Consequently, this work effectively resolves the scalability bottleneck inherent in large-scale hypergraph inference.

Abstract

Complex systems are routinely measured and represented through pairwise networks, even when the underlying interactions involve more than two units at once. Recovering this latent hypergraph structure from pairwise measurements is a fundamental inverse problem, but as the space of candidate hyperedges grows exponentially with system size, scalable hypergraph reconstruction at arbitrary interaction orders is out of reach for existing methods. Here we cast hypergraph reconstruction as a local signal-to-noise discrimination problem and use this locality to build a fast algorithm that reconstructs hypergraphs up to any interaction order. Across diverse synthetic and real-world systems our method achieves a high recovery accuracy of latent hypergraph structure while reconstructing hypergraphs up to orders of magnitude more quickly than current approaches. Our approach also yields an information-theoretic detectability boundary that sharply predicts which higher-order interactions are recoverable from pairwise measurements.

Problem

• higher-order interactions
• hypergraph reconstruction
• pairwise networks
• inverse problem
• scalability

Innovation

• Hypergraph reconstruction
• Higher-order interactions
• Signal-to-noise discrimination
• Scalable algorithm
• Detectability boundary