Beyond Dense Tensors: Exact Evaluation of Spectral Hypergraph Layers

Spectral hypergraph neural networks encode each hyperedge in a dense adjacency tensor, but their storage grows as the number of vertices raised to the size of the largest hyperedge, which makes them prohibitively expensive even on modest hypergraphs. We show that this cost is avoidable for the T-Spectral layer as released, whose readout sums all output slices of the t-product. We eliminate the tensor intermediates algebraically and evaluate the layer directly from node–hyperedge incidence data, preserving its output, normalisation and treatment of repeated hyperedges. After preprocessing, propagation takes time linear in the number of vertices and incidence entries for a fixed feature width, and neither the adjacency tensor nor its pairwise expansion is ever built. The same derivation reveals an expressivity limit already present in the original layer: on a labelled Pasch configuration, two differently labelled hypergraphs induce identical effective operators, which forces chance-level accuracy on a balanced task whose labels are recoverable from the incidence structure. Exact evaluation inherits this limit. Together, these results remove the dense-tensor barrier to evaluating the layer on larger hypergraphs and identify the structural distinctions that require a richer architecture.