图神经网络（更准确地说应该是GCN）往往容易面临over-smoothing的问题，即同一连通分量内的节点的表征会趋向于收敛到同一个值，过去的一些方法有：skip connections, global pooling, randomly dropping edges during training time等。本文考虑结点信息的传递方向，能够高效地远距离传递信息，进而解决该问题。
An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.
However, to the best of our knowledge, there are currently no methods that allow asymmetric graph kernels that are dependent on the full graph structure or directional flows. They either depend on local structures or local features.
Our method distinguishes itself from other spectral GNNs since the literature usually uses the low frequencies to
estimate local Fourier transforms in the graph.
Most of the improvement is attributed to the directional derivative aggregator, highlighting our method’s ability to capture directional high-frequency signals in graphs.
One of the biggest limitations of current GNN methods compared to CNNs is the inability to do message passing in a specific direction such as the horizontal one in a grid graph.
文章提出一种具有指向性的图神经网络（Directional Graph Networks，DGN），如下图所示，首先计算拉普拉斯矩阵的前k个特征向量（图中b），在计算相邻结点之间的梯度（c，实际上就是作差），然后再根据梯度来创建聚合矩阵，后面再与输入X相乘，层叠地计算。我认为其中的核心点是（c），通过结点的特征向量之间的差来反映图中结点信息传播的方向。作者声称，DGN能够在图中更好地传递有效信息，比1-WL Test有更好的表达能力，同时比以往的图神经网络在各个实验数据集上有更好的结果。（目前这版是arXiv的，有另一版ICLR的看着没什么区别，等ICML的出来再看看有没有大改或者新东西）
信息
1 学习到的新东西：
计算稀疏图的前k个特征向量的时间复杂度可以到O(kE)，其中E是边的数量。之前一直了解到的特征分解的复杂度会特别高，文章提到，通过Lanczos算法可以在O(kE)的复杂度内求解前k个特征向量。
Weisfeiler-Lehman Test：检验两个图是否同构的算法，一维的Weisfeiler-Lehman算法如下：
Weisfeiler-Lehman算法在大多数的图上都会收敛到一个唯一的特征集合。因此，对于大多数的图，Weisfeiler-Lehman算法得到的特征能够作为图是否同构的判别依据，也即WL Test。
一维Weisfeiler-Lehman算法在形式上跟GCN等图神经网络很像，都是根据邻居结点的聚合来更新结点，不同点在于图卷积等操作并不能保证函数的单射性。检测图的同构一直是个复杂的问题，目前没有多项式的算法能解决它，而Weisfeiler-Lehman算法是一个多项式的算法，能够在大多数情况下有效。因此，WL Test也经常被拿来对比图神经网络的表达能力（即分辨图结构的能力）。
本文表示，DGN的表达（expressive）能力要优于一维的WL Test（1-WL Test），因此也就优于一般的图神经网络。
在图神经网络中，对方向性的感知是有必要的，一方面可以更好地辨别图的结构，一方面相当于是引入了更多信息，提高模型的表示能力。
2 通过Related Work了解到了哪些知识
（本文没有写什么Related Work，ICML版估计有，到时看情况再更新）
3 实验验证任务，如果不太熟悉，需要简单描述
4 在你认知范围内，哪些其它任务可以尝试
类比TextGCN，可以用于NLP的任务？
5 好的句子
An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.
However, to the best of our knowledge, there are currently no methods that allow asymmetric graph kernels that are dependent on the full graph structure or directional flows. They either depend on local structures or local features.
Our method distinguishes itself from other spectral GNNs since the literature usually uses the low frequencies to estimate local Fourier transforms in the graph.
Most of the improvement is attributed to the directional derivative aggregator, highlighting our method’s ability to capture directional high-frequency signals in graphs.
One of the biggest limitations of current GNN methods compared to CNNs is the inability to do message passing in a specific direction such as the horizontal one in a grid graph.
6 References