arXiv:2606.10071cs.LGcs.AI2026-06

提出动态正交框架的时序图神经网络,精准建模节点角色演化。

Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

论文配图:Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport
图 1 · 摘自论文原文
  • 为每个节点配备随时间变化的正交坐标系,通过显式传输比较状态
  • 在多个时序链接预测数据集上超越现有方法,尤其擅长节点角色异质性强的场景
  • 适合研究动态网络中角色演化与几何结构建模的学者

我们提出时间层形神经网络(TSNN),一种时序链接预测框架,为每个节点配备随时间变化的正交基,并在显式传输至局部坐标系后比较节点状态。与现有在共享全局嵌入空间中运行的连续时间图模型不同,TSNN通过动态局部帧建模节点特异性且演化的交互语义。模型通过高效的低秩Householder乘积参数化节点帧,帧更新时精确保持隐藏状态,采用几何残差解码器,以传输距离为锚点学习残差修正。所有计算严格因果,仅使用事件前的历史信息。我们证明对称度归一化层形拉普拉斯算子与对称归一化图拉普拉斯算子正交相似,在随机游走归一化形式下于对应度度量中类似;TSNN使用的全活跃、特征缩放扩散恰好是组合层形狄利克雷能量上的度量梯度步,具备无度数单调下降和非扩张保证。帧漂移仅线性扰动更新。在TGB v2链接预测与时序异质排行榜,以及DGB基准套件上,TSNN在多数基准上匹配或超越最强先前方法,尤其在节点角色异质性强的图中提升显著。消融实验验证了动态帧、正交传输与几何残差解码的独立贡献。

原文摘要 · Abstract (English)

We introduce Temporal Sheaf Neural Networks (TSNN), a temporal link prediction framework that equips each node with a time-varying orthogonal frame and compares node states only after explicit transport between local coordinate systems. In contrast to existing continuous-time graph models that operate in a shared global embedding space, TSNN models node-specific and evolving interaction semantics through dynamic local frames. The model parameterizes per-node frames via efficient low-rank Householder products, preserves stored hidden states exactly under frame updates, and uses a geometric-residual decoder that anchors predictions on transported distances while learning residual corrections. All computations are strictly causal and use only the pre-event history. We show that the symmetric degree-normalized sheaf Laplacian is orthogonally similar to the symmetric normalized graph Laplacian, with the random-walk normalized form similar in the corresponding degree metric; the full-active, feature-scaled diffusion used by TSNN is exactly a metric-gradient step on the combinatorial sheaf Dirichlet energy, with a degree-free monotone-descent and non-expansiveness guarantee. Frame drift perturbs updates only linearly. Across TGB v2 link-prediction and temporal-heterogeneous leaderboards, together with the DGB benchmark suite, TSNN matches or surpasses the strongest prior methods on most benchmarks, with the largest improvements on graphs exhibiting strong node-role heterogeneity. Ablations confirm the distinct benefit of dynamic frames, orthogonal transport, and geometric-residual decoding.

时序图神经网络动态框架几何学习

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