Review of Artificial Neural HyperNetworks and SuperHyperNetworks Based on Hypergraphs, SuperHypergraphs, and Powersets
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Hypernetworks connect multiple nodes via hyperedges, modeling higher‐order group relationships. SuperHyperNetworks build on this by drawing nodes and edges from nested powersets, capturing multi‐level hierarchies with weighted links. A feedforward artificial neural network is a layered model in which neuron activations flow unidirectionally through weighted pairwise connections. In this paper, we introduce two extensions of this model using HyperGraph and SuperHyperGraph theory: the Artificial Neural HyperNetwork and the Artificial Neural SuperHyperNetwork. The Artificial Neural HyperNetwork replaces standard edges with weighted hyperedges, allowing activations to propagate nonlinearly through multi‐neuron groupings across layers. The Artificial Neural SuperHyperNetwork further generalizes this approach by using nested superhyperedges to transmit activations through hierarchically grouped neurons over multiple layers.