Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs. Recently, deep graph networks have been employed as efficient, data-driven surrogate models for predicting properties of complex systems represented as graphs. These models rely on a local and iterative message passing strategy that should, in principle, capture long-range information without explicitly modeling the corresponding interactions. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. This work proposes a general framework that learns to mitigate these limitations: within a variational inference framework, we endow message passing architectures with the ability to freely adapt their depth and filter messages along the way. With theoretical and empirical arguments, we show that this simple strategy better captures long-range interactions, by surpassing the state of the art on five node and graph prediction datasets suited for this problem. Our approach consistently improves the performances of the baselines tested on these tasks. We complement the exposition with qualitative analyses and ablations to get a deeper understanding of the framework's inner workings.

翻译：长程相互作用是众多科学领域正确描述复杂系统的关键。然而，将长程相互作用纳入计算所需付出的代价是整体计算成本的急剧增加。近年来，深度图网络已被用作高效的数据驱动替代模型，用于预测以图形式表示的复杂系统的属性。这些模型依赖于局部迭代的消息传递策略，该策略原则上应能捕捉长程信息，而无须显式建模相应相互作用。在实践中，大多数深度图网络因（同步）消息传递的内在局限（即过平滑、过挤压和欠传播）而无法真正建模长程依赖关系。本研究提出一个通用框架，通过学习来缓解这些局限：在变分推断框架内，我们赋予消息传递架构沿传播路径自由调整深度与过滤消息的能力。通过理论与实证论证，我们表明这一简单策略能更好捕捉长程相互作用，在五个适用于该问题的节点与图预测数据集上超越现有最优方法。我们的方法持续提升了这些任务中基线模型的性能。为深入理解框架内部机制，我们还辅以定性分析与消融实验来完善论述。