Learning over Positive and Negative Edges with Contrastive Message Passing

2026-05-18

AI Summary

This work addresses the limitation of conventional graph neural networks, which rely solely on positive edges for message passing and overlook the discriminative information embedded in negative edges—i.e., absent connections—particularly under conditions of low label rates, high homophily, or dense edge structures. The authors propose a Contrastive Message Passing (CMP) framework that, for the first time, theoretically establishes the potential of negative edges to yield significant information gain under specific conditions. CMP introduces a differentiable architecture that explicitly models both positive and negative edges in a unified manner: propagating similarity over positive edges and dissimilarity over negative edges. A learnable, soft positive semi-definite constraint is incorporated to apply distinct transformations to positive and negative connections. Experiments demonstrate that, in low-label settings across multiple synthetic and real-world datasets, CMP substantially outperforms existing baselines when negative edges are informative.

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.

Problem

• negative edges
• graph representation learning
• message passing
• homophily
• low-label learning

Innovation

• Contrastive Message Passing
• negative edges
• graph neural networks
• positive semidefinite constraints
• homophily