1 Title

        ADAPTIVE GRAPH DIFFUSION NETWORKS（Chuxiong Sun, Jie Hu, Hongming Gu, Jinpeng Chen, Mingchuan Yang）【2022】

2 Conclusion

        This study proposes the Adaptive Graph Diffusion Networks (AGDNs) which perform multi-layer generalized graph diffusion in different feature spaces with moderate complexity and runtime. Standard graph diffusion methods combine large and dense powers of the transition matrix with predefined weighting coefficients. Instead, AGDNs combine smaller multi-hop node representations with learnable and generalized weighting coefficients. It proposes two scalable mechanisms of weighting coefficients to capture multi-hop information: Hop-wise Attention (HA) and Hop-wise Convolution (HC).

3 Good Sentences

        1、However, unlike the deep models in the Computer Vision (CV) domain, the deep GNNs  will encounter the over-smoothing problem, resulting in significant performance degradation. The model cannot distinguish the node representations, which become nearly identical after long-range message passing. Deep GNNs may contain many feature transformations since a GNN layer usually couples a graph convolution operator and a feature transformation（The problems of GNNs meet）
        2、. However, GDC lacks flexibility since its weighting coefficients are predefined and fixed for different nodes and feature channels. Moreover, GDC cannot improve link prediction performance. A more efficient but equivalent way of calculating the graph diffusion is to calculate multi-hop node representations iteratively and combine them. Some methods perform this memory-efficient graph diffusion in each layer without calculating the explicit diffusion matrix.（The limitations of related works GDC that has not been well studied）
        3、The Scalable Inception Graph Neural Network (SIGN） encodes and concatenates multi-hop representations. However, as a trade-off between efficiency and accuracy, the simple decoupled architecture limits model capacity because all graph convolution operators are
restricted in the same feature space. There are no intermediate transformations between graph convolution operators（The shortcomings of Decoupled GNNs）

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本文提出了自适应图扩散神经网络(AGDNs ),其广义图扩散与两种可学习和可扩展的加权系数机制相关联:逐跳注意(HA)和逐跳卷积(HC)。从MPNNs到GDNs，感受野被扩大，而不增加额外的变换或解耦模型结构。不同特征空间中的多层图扩散可以有助于模型容量。HA引入了逐跳和逐节点的加权系数。HC可以直接学习逐跳和逐信道加权系数。

这篇文章本身感觉没什么用，倒是做了一些类似综述的工作可以看看

相关工作：

        Residual GNNs：通过残差链接,GNNs解决了过拟合和过平滑问题

        Graph diffusion：图卷积描述为转移矩阵和节点特征/表示矩阵之间的矩阵乘法。然后，图扩散用扩散矩阵代替转移矩阵，该扩散矩阵是转移矩阵的幂与沿跳标准化的加权系数的线性组合。加权系数对于平衡浅层和深层信息的重要性至关重要。个性化PageRank (PPR)和热核(HK) 是两种流行的预定义加权系数。它们都遵循这样的先验，即较远的相邻节点比较近的相邻节点具有更少的影响。加权系数也可以是使用标签传播的类似可训练参数。注意力行走联合优化了节点嵌入和加权系数。

        Decoupled GNNs：为了使用浅特征变换执行深图卷积，解耦GNNs将图卷积运算符和特征变换解耦。如DCNN、SDC

        Explicit diffusion matrix: Graph Diffusion Convolution：作为增加输入数据的预处理方法，图形扩散卷积(GDC) [19]计算显式扩散矩阵。虽然GDC控制最终扩散矩阵的稀疏性，但中间显式的高次幂转移矩阵仍被保持，这限制了它的可扩展性。PPR和HK有近似的方法来缓解这个信息损失的问题。此外，加权系数是预定义的，并且对于所有节点、通道和层都是相同的，这可能会限制模型性能。GDC不能在可学习转移矩阵的预处理中计算。此外，GDC不能提高链路预测性能

         Implicit diffusion matrix: Graph Diffusion Networks：图扩散网络（gdn）执行隐式图扩散，从每层中的节点特征或表示矩阵开始进行从右到左的矩阵乘法。首先，GDNs依次计算多跳表示矩阵。然后，他们整合这些矩阵，而无需维护高维扩散矩阵。这种范式更节省内存，因为高阶聚合特征矩阵比高次幂转换矩阵小得多