Beyond pairwise interactions: Accurate forecasting of co-evolutionary spreading on higher-order networks

Abstract

Many co-evolutionary spreading processes involve higher-order interactions, yet the consequences of approximating them through pairwise representations remain insufficiently understood. Here, we uncover distinctive prediction failures of pairwise graph neural networks during node-level one-step conditional transition-probability prediction on simplicial complexes. Patterns of bias between Att-GNN predictions and the true transition probabilities show ordered diagonal stratification in homogeneous networks and apparently disordered scattering in long-tailed networks, with bias persisting even at nodes with negligible second-order connectivity. Bias direction depends systematically on the relative numbers of active 1- and 2-simplex transmission channels, which jointly characterize local exposure. We interpret these phenomena as higher-order truncation bias arising from compensatory learning. Omitted simplicial contributions are absorbed into a shared pairwise mapping whose statistical compromise yields excessive or insufficient compensation across local exposure conditions. To address this, we propose Att-HGNN, a topology-adaptive higher-order attention model that explicitly aggregates simplicial interactions through node-specific queries and structure-specific keys and values. Across competitive, cooperative, and asymmetric dynamics simulated on synthetic and empirical contact-derived topologies, Att-HGNN empirically reduces the observed prediction bias. Ten-seed comparisons between matched pairwise and higher-order variants of four GNN families on SC-ER and SC-SF networks show consistent benefits from higher-order aggregation, with Att-HGNN achieving the strongest overall performance among eight models in Pearson correlation and probability MSE.