mHC-GNN: Manifold-Constrained Hyper-Connections for Graph Neural Networks

Graph Neural Networks (GNNs) suffer from over-smoothing in deep architectures and expressiveness bounded by the 1-Weisfeiler-Leman (1-WL) test. We adapt Manifold-Constrained Hyper-Connections (mHC), recently proposed for Transformers, to graph neural networks. Our method, mHC-GNN, expands node representations across $n$ parallel streams and constrains stream-mixing matrices to the Birkhoff polytope via Sinkhorn-Knopp normalization. We prove that mHC-GNN exhibits exponentially slower over-smoothing (rate $(1-)^L/n$ vs.\ $(1-)^L$) and can distinguish graphs beyond 1-WL. Experiments on 10 datasets with 4 GNN architectures show consistent improvements. Depth experiments from 2 to 128 layers reveal that standard GNNs collapse to near-random performance beyond 16 layers, while mHC-GNN maintains over 74\ Ablations confirm that the manifold constraint is essential: removing it causes up to 82\