Resolving Node Identifiability in Graph Neural Processes via Laplacian Spectral Encodings

TL;DR

This paper introduces a Laplacian spectral encoding for graph neural networks that enhances their ability to distinguish nodes, overcoming limitations of existing methods and demonstrating improved performance on chemical graph tasks.

Contribution

The paper provides a rigorous theoretical foundation for spectral encodings that achieve node identifiability and surpass Weisfeiler-Lehman constrained architectures.

Findings

Spectral encoding is invariant to eigenvector sign flips and basis rotations.

The encoding enables node identifiability from a constant number of observations.

Empirical results show improved ROC and F1 scores on drug interaction tasks.

Abstract

Message passing graph neural networks are widely used for learning on graphs, yet their expressive power is limited by the one-dimensional Weisfeiler-Lehman test and can fail to distinguish structurally different nodes. We provide rigorous theory for a Laplacian positional encoding that is invariant to eigenvector sign flips and to basis rotations within eigenspaces. We prove that this encoding yields node identifiability from a constant number of observations and establishes a sample-complexity separation from architectures constrained by the Weisfeiler-Lehman test. The analysis combines a monotone link between shortest-path and diffusion distance, spectral trilateration with a constant set of anchors, and quantitative spectral injectivity with logarithmic embedding size. As an instantiation, pairing this encoding with a neural-process style decoder yields significant gains on a drug-drug interaction task on chemical graphs, improving both the area under the ROC curve and the F1 score and demonstrating the practical benefits of resolving theoretical expressiveness limitations with principled positional information.