Learn to Jump: Adaptive Random Walks for Long-Range Propagation through Graph Hierarchies

Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this challenge. Our method introduces learnable transition probabilities that decide whether the walk should prefer the original graph or travel across hierarchical shortcuts. On a synthetic long-range task, we demonstrate that our approach can exceed the theoretical bound that constrains traditional approaches operating solely on the original topology. Specifically, walks that prefer the hierarchy achieve the same performance as longer walks on the original graph. These preliminary findings open a promising direction for efficiently processing large graphs while effectively capturing long-range dependencies.