Yoshihiro Maruyama

Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks

We develop order-equivariant neural networks (OENN), which generalize standard graph message passing and sheaf neural networks via the face-poset viewpoint. We (i) characterize all linear order-equivariant maps, (ii) build OENN layers, and (iii) prove a universal approximation theorem (UAT) for cont…