PathMLP: Smooth path towards high-order homophily.

Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance. Intriguingly, from the observation of heterophilous data, we notice that certain high-order information exhibits higher homophily, which motivates us to involve high-order information in node representation learning. However, common practices in GNNs to acquire high-order information mainly through increasing model depth and altering message-passing mechanisms, which, albeit effective to a certain extent, suffer from three shortcomings: (1) over-smoothing due to excessive model depth and propagation times; (2) high-order information is not fully utilized; (3) low computational efficiency.