Learning Directed Knowledge Using Higher-Ordered Neural Networks: Building a Predictive Framework

Most graph learning methods remain limited to undirected, pairwise interactions, restricting their ability to capture the multi-entity and directional relationships common in real-world systems. We propose the Directed Higher-Ordered Neural Network (HONN) framework that introduces directionality into hypergraph learning through flexible spectral Laplacian formulations. Unlike fixed-Laplacian methods such as the Generalized Directed Hypergraph Neural Network (GeDi-HNN), a tunable q-parameter in our framework balances local identity preservation with global diffusion, enabling robust and generalizable feature propagation. Experiments on five benchmark datasets show that HONN consistently matches or outperforms state-of-the-art baselines, achieving 84% on NTU-2012, 87.4% on WebKB Texas, and 86.2% on Cornell, while maintaining computational efficiency. Ablation studies confirm the crucial role of Laplacian selection, activation functions, and q-tuning in shaping model performance. By unifying directionality and higher-order reasoning, HONN provides a scalable foundation for predictive modeling in domains such as knowledge graphs, spatio-temporal networks, and recommendation systems.