EqDynHyper Equivariant Dynamic Hypergraph for Group-Level Motion Prediction and Group Discovery

Multi-agent motion forecasting must respect geometric symmetries while modeling both pairwise interactions and emergent collective group dynamics. Existing Euclidean-equivariant predictors rely on pairwise message passing and have no native group-level primitive, whereas hypergraph forecasters that do model groups are not Euclidean-equivariant. We present EqDynHyper, an equivariant hypergraph network with two disentangled outputs: trajectory forecasts, whose accuracy is insensitive to grouping quality and whose efficiency comes from equivariant centroid aggregation over hyperedges, and agent-group partitions, recovered without membership supervision through Euclidean-invariant soft hyperedge assignments. Building on the scalar-vector separation of GVP-GNN and PaiNN, we add an explicit affine Point type and the closure rules needed for higher-order aggregation, so that trajectories are equivariant and assignments invariant by construction. Assignments are computed once by default and can optionally be re-inferred at every layer. We find that competitive (softmax) normalization of the assignment matrix, rather than auxiliary entropy losses, is what prevents hyperedge collapse. EqDynHyper replaces $O(N^2)$ vector-valued pairwise message passing with $O(NK)$ hyperedge aggregation; a scalar pairwise topology term remains $O(N^2)$, and at $N=400$ inference is $9.4\times$ faster with $3.75\times$ less memory than EqMotion. On synthetic collective dynamics EqDynHyper lowers ADE by $2.9\times$ relative to EqMotion, and on ETH-UCY by 5.0 percent under a unified retraining protocol; on bond-dominated MD17 molecules it is less accurate than pairwise models, which we report together with other failure modes.