Topological Readouts of Learned Positional Filtrations for Hypergraph Classification

Hypergraph neural networks perform hypergraph classification by message passing, which on graphs has been combined with positional encodings and persistent homology. Hypergraphs admit several expansions; a clique expansion can map hypergraphs whose star expansions differ in cycle rank to the same graph. On a widely used public benchmark, reported accuracies on two social collections lie near majority-class rates. Descriptors that combine positional and topological information on the star expansion may capture label information that these methods miss. We propose HyLPF: positional states initialized with random-walk positional encodings propagate over the star expansion, defining learned filtrations whose persistent homology, including cycle rank and essential-vertex flags, alone feeds the classifier. HyLPF achieves the best overall accuracy on the benchmark's four collections, ranking first on three and second on the fourth, with its configuration fixed before evaluation on new splits of the benchmark and under its split protocol and metric. On one of the social collections, matched controls show that the cycle rank and flags, with the weights reading them, carry label information, while merge values and cycle values add no detectable accuracy beyond them.