High-order Graph Neural Networks (HO-GNNs) have been developed to infer
consistent latent spaces in the heterophilic regime, where the label
distribution is not correlated with the graph structure. However, most of the
existing HO-GNNs are hop-based, i.e., they rely on the powers of the transition
matrix. As a result, these architectures are not fully reactive to the
classification loss and the achieved structural filters have static supports.
In other words, neither the filters' supports nor their coefficients can be
learned with these networks. They are confined, instead, to learn combinations
of filters. To address the above concerns, we propose Diffusion-jump GNNs a
method relying on asymptotic diffusion distances that operates on jumps. A
diffusion-pump generates pairwise distances whose projections determine both
the support and coefficients of each structural filter. These filters are
called jumps because they explore a wide range of scales in order to find bonds
between scattered nodes with the same label. Actually, the full process is
controlled by the classification loss. Both the jumps and the diffusion
distances react to classification errors (i.e. they are learnable).
Homophiliation, i.e., the process of learning piecewise smooth latent spaces in
the heterophilic regime, is formulated as a Dirichlet problem: the known labels
determine the border nodes and the diffusion-pump ensures a minimal deviation
of the semi-supervised grouping from a canonical unsupervised grouping. This
triggers the update of both the diffusion distances and, consequently, the
jumps in order to minimize the classification error. The Dirichlet formulation
has several advantages. It leads to the definition of structural heterophily, a
novel measure beyond edge heterophily. It also allows us to investigate links
with (learnable) diffusion distances, absorbing random walks and stochastic
diffusion.

提出使用渐进扩散差距的方法进行跳跃的扩散 - hops exploration，从而产生更具有动态支持的结构过滤器，建议用 Dirichlet 问题作为一种方法来在异类亲缘而不相关的标签分布的情况下学习逐段平滑的积淀空间，并使用 (可学习的) 渐进扩散距离、吸收随机漫步和 (具有可学习性) 随机扩散进行链接探索。