Graph neural networks have achieved great success in learning node
representations for graph tasks such as node classification and link
prediction. Graph representation learning requires graph pooling to obtain
graph representations from node representations. It is challenging to develop
graph pooling methods due to the variable sizes and isomorphic structures of
graphs. In this work, we propose to use second-order pooling as graph pooling,
which naturally solves the above challenges. In addition, compared to existing
graph pooling methods, second-order pooling is able to use information from all
nodes and collect second-order statistics, making it more powerful. We show
that direct use of second-order pooling with graph neural networks leads to
practical problems. To overcome these problems, we propose two novel global
graph pooling methods based on second-order pooling; namely, bilinear mapping
and attentional second-order pooling. In addition, we extend attentional
second-order pooling to hierarchical graph pooling for more flexible use in
GNNs. We perform thorough experiments on graph classification tasks to
demonstrate the effectiveness and superiority of our proposed methods.
Experimental results show that our methods improve the performance
significantly and consistently.

本论文提出使用二阶汇集技术作为图聚合技术，结合双线性映射和注意力机制的二阶汇集方法性能优越，在图分类任务中取得了显著的表现提升。

图神经网络的二阶池化

Second-Order Pooling for Graph Neural Networks

Traditional neural networks assume vectorial inputs as the network is
arranged as layers of single line of computing units called neurons. This
special structure requires the non-vectorial inputs such as matrices to be
converted into vectors. This process can be problematic. Firstly, the spatial
information among elements of the data may be lost during vectorisation.
Secondly, the solution space becomes very large which demands very special
treatments to the network parameters and high computational cost. To address
these issues, we propose matrix neural networks (MatNet), which takes matrices
directly as inputs. Each neuron senses summarised information through bilinear
mapping from lower layer units in exactly the same way as the classic feed
forward neural networks. Under this structure, back prorogation and gradient
descent combination can be utilised to obtain network parameters efficiently.
Furthermore, it can be conveniently extended for multimodal inputs. We apply
MatNet to MNIST handwritten digits classification and image super resolution
tasks to show its effectiveness. Without too much tweaking MatNet achieves
comparable performance as the state-of-the-art methods in both tasks with
considerably reduced complexity.

提出了一种矩阵神经网络（MatNet），通过双线性映射从上一层单元中感知总结信息，并方便地扩展到多模输入，应用于 MNIST 手写数字分类和图像超分辨率任务中，具有与最先进方法可比较的性能和大大降低的复杂性。