{"ID":2822664,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.02451","arxiv_id":"2601.02451","title":"mHC-GNN: Manifold-Constrained Hyper-Connections for Graph Neural Networks","abstract":"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)~\\citep{xie2025mhc}, 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 $(1-γ)^{L/n}$ vs.\\ $(1-γ)^L$) 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\\% accuracy even at 128 layers, with improvements exceeding 50 percentage points at extreme depths. Ablations confirm that the manifold constraint is essential: removing it causes up to 82\\% performance degradation. Code is available at \\href{https://github.com/smlab-niser/mhc-gnn}{https://github.com/smlab-niser/mhc-gnn}","short_abstract":"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)~\\citep{xie2025mhc}, recently proposed for Transformers, to graph neural networks. Our method, mHC-GNN, expands node repre...","url_abs":"https://arxiv.org/abs/2601.02451","url_pdf":"https://arxiv.org/pdf/2601.02451v1","authors":"[\"Subhankar Mishra\"]","published":"2026-01-05T17:25:45Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Graph Neural Network\",\"Transformer\"]","has_code":false,"code_links":[{"ID":605435,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2822664,"paper_url":"https://arxiv.org/abs/2601.02451","paper_title":"mHC-GNN: Manifold-Constrained Hyper-Connections for Graph Neural Networks","repo_url":"https://github.com/smlab-niser/mhc-gnn","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}