Spectral Maps for Learning on Subgraphs

TL;DR

This paper introduces a spectral map representation for graph learning that improves robustness and interpretability, especially in scenarios with topological changes or undefined node correspondences, leading to better performance with less computation.

Contribution

The authors propose a spectral representation for graph maps that enhances robustness, interpretability, and efficiency in graph learning tasks, especially under topological variations.

Findings

Spectral maps improve robustness to topological changes.

Spectral maps enable better interpretability of graph correspondences.

The approach achieves comparable or better performance with reduced computational cost.

Abstract

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and modified graphs. Classically, these maps are represented as binary node-to-node correspondence matrices and used as-is to transfer node-wise features between the graphs. In this paper, we argue that simply changing this map representation can bring notable benefits to graph learning tasks. Drawing inspiration from recent progress in geometry processing, we introduce a spectral representation for maps that is easy to integrate into existing graph learning models. This spectral representation is a compact and straightforward plug-in replacement and is robust to topological changes of the graphs. Remarkably, the representation exhibits structural properties that make it interpretable, drawing an analogy with recent results on smooth manifolds. We demonstrate the benefits of incorporating spectral maps in graph learning pipelines, addressing scenarios where a node-to-node map is not well defined, or in the absence of exact isomorphism. Our approach bears practical benefits in knowledge distillation and hierarchical learning, where we show comparable or improved performance at a fraction of the computational cost.