Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables

2026-05-13

AI Summary

This work addresses the limitations of signal propagation in graph neural networks, which are prone to oversmoothing and over-squashing, thereby hindering directed information flow across distant regions. Inspired by quantum mechanics, the study introduces observables—borrowed from quantum theory—into the spectral graph neural network framework to formally characterize signal position, concentration, and directional propagation on graphs. Building upon this formulation, the authors propose Schrödinger GNN, a novel spectral GNN architecture. Theoretical analysis demonstrates that Schrödinger GNN significantly enhances directional signal routing compared to standard spectral GNNs, effectively mitigating information loss during message passing.

Abstract

Graph Neural Networks (GNNs) perform computations on graphs by routing the signal between graph regions using a graph shift operator or a message passing scheme. Often, the propagation of the signal leads to a loss of information, where the signal tends to diffuse across the graph instead of being deliberately routed between regions of interest. Two notions that depict this phenomenon are oversmoothing and oversquashing. In this paper, we propose an alternative approach for modeling signal propagation, inspired by quantum mechanics, using the notion of observables. Specifically, we model the place in the graph where the signal lies, how much the signal is concentrated there, and how much of the signal is propagated towards a location of interest when applying a GNN. Using these new concepts, we prove that standard spectral GNNs have poor signal propagation capabilities. We then propose a new type of spectral GNN, termed Schrödinger GNN, which we show has a superior capacity to route the signal across the graph.

Problem

• signal propagation
• oversquashing
• oversmoothing
• Graph Neural Networks
• information loss

Innovation

• observables
• signal propagation
• oversquashing
• spectral GNNs
• Schrödinger GNN