Learning over Positive and Negative Edges with Contrastive Message Passing

TL;DR

This paper introduces Contrastive Message Passing (CMP), a novel graph neural network architecture that leverages both positive and negative edges to improve learning, especially in low-label, high-homophily, and dense graph settings.

Contribution

The paper provides a theoretical analysis of negative edges' value and proposes CMP, which effectively incorporates negative edges into message passing for enhanced graph representation learning.

Findings

CMP outperforms baselines in low-label regimes with informative negative edges.

Theoretical analysis shows negative edges provide significant information gain under certain conditions.

CMP applies soft positive semidefinite constraints to differentiate positive and negative edge influences.

Abstract

Conventional approaches to learning on graphs involve message passing along existing (i.e., positive) edges to update node features. However, these approaches often disregard the potentially valuable information contained in the absence (i.e., negative) of edges. Here, we theoretically analyze the value of negative edges in graph representations and prove that in settings of low label rates, high homophily, and high edge density, access to negative edges provides significant information gain over using only positive edges. Motivated by this insight, we introduce Contrastive Message Passing (CMP), a general message passing architecture that enable graph neural network layers to reason over positive and negative edges. By imposing soft positive semidefinite constraints on the learnable weights, our approach differentially applies similarity-preserving transformations to positively connected nodes and dissimilarity-inducing transformations to negatively connected nodes. Over simulated and real datasets in varying data regimes, CMP consistently outperforms baselines in low-label settings when negative edges are informative.