The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing as a special case. Most approaches to mitigate over-smoothing extend common message-passing schemes, e.g., the graph convolutional network, by utilizing residual connections, gating mechanisms, normalization, or regularization techniques. Our work contrarily proposes to directly tackle the cause of this issue by modifying the message-passing scheme and exchanging different types of messages using multi-relational graphs. We identify a sufficient condition to ensure linearly independent node representations. As one instantion, we show that operating on multiple directed acyclic graphs always satisfies our condition and propose to obtain these by defining a strict partial ordering of the nodes. We conduct comprehensive experiments that confirm the benefits of operating on multi-relational graphs to achieve more informative node representations.

翻译：消息传递神经网络（MPNN）拟合图上复杂函数的能力受到限制，因为大多数图卷积在所有特征通道上放大相同信号，这种现象称为秩崩溃，而过平滑是其特例。缓解过平滑的大多数方法通过利用残差连接、门控机制、归一化或正则化技术来扩展常见的消息传递方案（如图卷积网络）。相反，我们的工作提出通过修改消息传递方案并使用多关系图交换不同类型的消息来直接解决此问题的根源。我们确定了一个确保节点表示线性独立的充分条件。作为一种具体实现，我们证明在多向有向无环图上操作始终满足我们的条件，并建议通过定义节点的严格偏序来获得这些图。我们进行了全面的实验，证实了在多关系图上操作可获得更具信息量的节点表示的益处。