用豪斯霍尔德矩阵探索过平滑问题
Exploring Oversmoothing with Householder Matrices
中文总结 AI 辅助
针对深度图神经网络的过平滑问题，提出HouseGNN模型，利用豪斯霍尔德反射器与GroupSort构建分段正交层，证明其核心性质以缓解过平滑。
中文摘要 AI 辅助
深度图神经网络（GNNs）存在过平滑问题，即随着网络深度增加，节点表示会逐渐坍缩至低信息子空间，原因是归一化图传播算子会被反复直接应用于隐藏表示。本研究探讨豪斯霍尔德图神经网络（HouseGNN），该模型不像标准GCN那样更新隐藏状态，而是仅用聚合的邻域消息估计反射方向，再通过豪斯霍尔德反射器结合GroupSort更新节点嵌入，生成分段正交层，可在每一层、每深度保留节点的欧氏范数。我们证明三个核心性质：（i）每个内部层保留节点级欧氏范数；（ii）豪斯霍尔德反射器对消息具有尺度和符号不变性；（iii）节点间的成对距离可通过节点级正交算子的不匹配发生变化。
英文摘要
Deep graph neural networks(GNNs) suffer from oversmoothing- a progressive collapse of node representation towards a low information subspace as network depth increases because the normalized graph propagation operator is repeatedly applied directly to the hidden representations. In this work we study Householder Graph Neural Network (HouseGNN). Rather than updating the hidden state like standard GCN, HouseGNN uses the aggregated neighbourhood message solely to estimate a reflection direction; the node embedding is then updated by a Householder reflector followed by GroupSort, yielding a piecewise orthogonal layer that preserves Euclidean norm at every node and at every depth. We prove three core properties: (i) every internal layer preserves the node-wise Euclidean norm; (ii) the Householder reflector is scale scale and sign-invariant in the message; and (iii) pairwise distance between nodes can change through mismatch between node-wise orthogonal operators.
