CoopHyperMoE: Membership Interpolation over an Expert Hypergraph for Molecular Graph Prediction

Graph mixture-of-experts (MoE) models adapt message passing to heterogeneous graph inputs, yet a top-K router must select experts even when every routing score is weak. We introduce CoopHyperMoE, a membership-based router that keeps node–expert affinities independent before selection. It periodically builds a hypergraph from similarities between routing vectors and, for low-membership inputs, interpolates non-anchor memberships from principal-component anchors in the active hyperedges. A normalized top-K gate is then computed from the revised memberships. We evaluate CoopHyperMoE with four fixed seeds and validation-selected checkpoints on ten molecular benchmarks: seven classification datasets and three regression datasets. Without a virtual node, CoopHyperMoE records a higher mean ROC-AUC than a locally reproduced GMoE on five of seven classification tasks and raises the seven-task average from 71.90 to 72.04; it also obtains the lowest local RMSE on Lipophilicity. Matched ablations on six classification datasets test interpolation, annealing, and the activation rule. A final-checkpoint audit finds no interpolation triggers on the BACE and Tox21 validation splits, limiting what these comparisons establish about the interpolation mechanism.