ResolvNet: A Graph Convolutional Network with multi-scale Consistency

TL;DR

ResolvNet is a novel graph neural network architecture designed to maintain multi-scale consistency, effectively propagating information across complex graph structures and across different resolutions, outperforming existing models.

Contribution

The paper introduces ResolvNet, a new GNN architecture that ensures multi-scale consistency both at node and graph levels, addressing limitations of existing models.

Findings

ResolvNet achieves superior performance on multiple real-world tasks.

It rigorously guarantees multi-scale consistency theoretically.

Outperforms baseline models significantly in experiments.

Abstract

It is by now a well known fact in the graph learning community that the presence of bottlenecks severely limits the ability of graph neural networks to propagate information over long distances. What so far has not been appreciated is that, counter-intuitively, also the presence of strongly connected sub-graphs may severely restrict information flow in common architectures. Motivated by this observation, we introduce the concept of multi-scale consistency. At the node level this concept refers to the retention of a connected propagation graph even if connectivity varies over a given graph. At the graph-level, multi-scale consistency refers to the fact that distinct graphs describing the same object at different resolutions should be assigned similar feature vectors. As we show, both properties are not satisfied by poular graph neural network architectures. To remedy these shortcomings, we introduce ResolvNet, a flexible graph neural network based on the mathematical concept of resolvents. We rigorously establish its multi-scale consistency theoretically and verify it in extensive experiments on real world data: Here networks based on this ResolvNet architecture prove expressive; out-performing baselines significantly on many tasks; in- and outside the multi-scale setting.