提出mHC-GNN，让图神经网络更深更准，突破传统模型过平滑瓶颈。
mHC-GNN: Manifold-Constrained Hyper-Connections for Graph Neural Networks
- 用双随机约束的多流混合机制，防止深层网络特征退化
- 128层下仍保持74%准确率，比普通GNN提升超50个百分点
- 适用于复杂异质图和超越1-WL测试的图区分任务
图神经网络在深层架构中面临过平滑问题，且表达能力受限于1-魏斯费勒-莱曼（1-WL）测试。本文将近期用于Transformer的流形约束超连接方法引入GNN，提出 exttt{mHC-GNN}。该方法通过 $n$ 个并行流扩展节点表示，并利用Sinkhorn-Knopp归一化将流间混合矩阵约束在双随机矩阵的Birkhoff多面体中。理论证明， exttt{mHC-GNN} 通过逐层残差下界缓解过平滑：节点对差异衰减速率为 $(1{-}ar{ ho})^L$（$ar{ ho}$ 衡量混合矩阵偏离单位阵程度），远慢于标准的 $(1{-}γ)^L$（$γ$ 为谱间隙）。该两阶段分析——$L < n$ 时保护正交子空间，$L \ geq n$ 时逐层收缩——提供了无依赖架构的速率保证。独立随机初始化下， exttt{mHC-GNN} 可通过保持流多样性实现超越1-WL的图区分能力。深度实验显示，标准GNN在超过16层后性能接近随机，而 exttt{mHC-GNN} 在128层仍保持74%以上准确率，极端深度下性能提升超50个百分点。消融实验表明，移除流形约束导致最高达82%的性能下降。在异质图（roman-empire, penn94, genius）和表达能力基准（EXP）上进一步验证了有效性。代码已开源。
原文摘要 · Abstract (English)
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, recently proposed for Transformers, to graph neural networks. Our method, \mhcgnn{}, expands node representations across $n$ parallel streams and constrains stream-mixing matrices to the Birkhoff polytope of doubly stochastic matrices via Sinkhorn-Knopp normalization. We prove that \mhcgnn{} mitigates over-smoothing via a layer-wise residual lower bound showing that node-pair differences decay at rate $(1{-}\varepsilon)^L$ (where $\varepsilon$ measures deviation of the mixing matrix from identity), far slower than the standard $(1{-}γ)^L$ collapse rate driven by the spectral gap $γ$. This two-regime analysis, via the protected orthogonal subspace for $L < n$ and the layer-wise contraction for $L \geq n$, provides architecture-agnostic rate guarantees absent from prior methods. With independent random stream initialization, \mhcgnn{} can distinguish graphs beyond 1-WL by maintaining stream diversity across layers via doubly stochastic mixing. Depth experiments spanning 2 to 128 layers reveal that standard GNNs collapse to near-random performance beyond 16 layers, while \mhcgnn{} maintains over 74\% accuracy at 128 layers, with improvements exceeding 50 percentage points at extreme depths. Ablations confirm that manifold constraints are essential: removing them causes up to 82\% performance degradation. Experiments on heterophilic graphs (roman-empire, penn94, genius) and expressiveness benchmarks (EXP) further validate the contribution. Code is available at https://github.com/smishra-lab/mhc-gnn
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