Recent works have shown that physics-inspired architectures allow the
training of deep graph neural networks (GNNs) without oversmoothing. The role
of these physics is unclear, however, with successful examples of both
reversible (e.g., Hamiltonian) and irreversible (e.g., diffusion) phenomena
producing comparable results despite diametrically opposed mechanisms, and
further complications arising due to empirical departures from mathematical
theory. This work presents a series of novel GNN architectures based upon
structure-preserving bracket-based dynamical systems, which are provably
guaranteed to either conserve energy or generate positive dissipation with
increasing depth. It is shown that the theoretically principled framework
employed here allows for inherently explainable constructions, which
contextualize departures from theory in current architectures and better
elucidate the roles of reversibility and irreversibility in network
performance.

本篇论文介绍了一些基于保结构动力系统的创新图神经网络结构，其中证明了这些结构能够保能量或随深度逐渐产生正的耗散。这一理论框架为可解释的构建提供了可能，并在阐明了可逆性和不可逆性在网络性能中的作用的同时，帮助解释了当前网络架构中的理论离题。