Graph neural networks compute node representations by performing multiple
message-passing steps that consist in local aggregations of node features.
Having deep models that can leverage longer-range interactions between nodes is
hindered by the issues of over-smoothing and over-squashing. In particular, the
latter is attributed to the graph topology which guides the message-passing,
causing a node representation to become insensitive to information contained at
distant nodes. Many graph rewiring methods have been proposed to remedy or
mitigate this problem. However, properly evaluating the benefits of these
methods is made difficult by the coupling of over-squashing with other issues
strictly related to model training, such as vanishing gradients. Therefore, we
propose an evaluation setting based on message-passing models that do not
require training to compute node and graph representations. We perform a
systematic experimental comparison on real-world node and graph classification
tasks, showing that rewiring the underlying graph rarely does confer a
practical benefit for message-passing.

本文针对图神经网络在传递节点特征时的过度平滑和过度压缩问题，提出了通过改变图结构解决该问题的方法，并给出了不需要训练就能计算节点和图表示的评估设置，结果表明重构底层图对消息传递很少有实际的好处。

图神经网络中的重连效果究竟有多大帮助？

Is Rewiring Actually Helpful in Graph Neural Networks?

One of the main challenges in solving time-dependent partial differential
equations is to develop computationally efficient solvers that are accurate and
stable. Here, we introduce a graph neural network approach to finding efficient
PDE solvers through learning using message-passing models. We first introduce
domain invariant features for PDE-data inspired by classical PDE solvers for an
efficient physical representation. Next, we use graphs to represent PDE-data on
an unstructured mesh and show that message passing graph neural networks
(MPGNN) can parameterize governing equations, and as a result, efficiently
learn accurate solver schemes for linear/nonlinear PDEs. We further show that
the solvers are independent of the initial trained geometry, i.e. the trained
solver can find PDE solution on different complex domains. Lastly, we show that
a recurrent graph neural network approach can find a temporal sequence of
solutions to a PDE.

通过应用图神经网络和消息传递模型，我们提出了一种有效的 PDE 求解方法，通过参数化控制方程，学习领域不变特征，构建线性 / 非线性 PDE 的准确求解器。