Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs

תקציר מקורי באנגליתarXiv:2608.28853v3 Announce Type: replace-cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how vector information can be transformed as it moves across a graph. We introduce \textsc{ESNN}, an Equivariant Sheaf Neural Network that enriches this interaction by learning directed, matrix-valued transport between neighboring vector features while preserving exact Euclidean equivariance. Rather than increasing the order of the representation, ESNN keeps scalar and vector features first-order and places the additional geometric flexibility in the edge transport itself. We characterize this transport theoretically, showing that when relative displacement is the only covariant geometric i