Learn When and Where to Connect: Adaptive Virtual Nodes for Dynamic Message Passing on Graphs

2026-06-01

AI Summary

This work addresses critical limitations in existing graph neural networks that employ virtual nodes—namely, their fixed connectivity patterns, restricted quantity, and neglect of collaborative relationships among nodes. To overcome these issues, we propose the MAVN framework, which introduces, for the first time, an end-to-end differentiable mechanism for dynamically inserting virtual nodes on demand. MAVN supports arbitrary node–virtual-node connection topologies and comes with theoretical expressiveness guarantees. The approach integrates seamlessly into the message-passing neural network (MPNN) paradigm through a dual-perspective scoring mechanism, a candidate virtual node pool selection strategy, and a dynamic message-passing architecture. Extensive experiments across nine real-world datasets demonstrate substantial performance gains over strong baselines, with improvements of up to 46.5% on key metrics.

Abstract

While Virtual Nodes (VNs) are often utilized in Message Passing Neural Networks (MPNNs) to facilitate effective message passing, existing VN-based methods have limitations, such as constraining all nodes to connect to the same number of VNs, fixing the connections before applying MPNNs, and connecting a node to a VN independently of the other nodes that connect to the same VN. We propose MAVN, an end-to-end differentiable MPNN framework that allows non-constrained connections between nodes and VNs and dynamically introduces VNs on demand in response to evolving node representations across layers. Specifically, MAVN learns to adaptively determine when (at which layer) and where (to which nodes) to introduce and connect VNs based on the relative importance of connections. From a pool of candidate VNs, MAVN selects the necessary VNs in each layer, where each selected VN is connected to a nonempty subset of nodes, guided by a dual-perspective scoring mechanism that jointly captures the nodes' preferences for VNs and the VNs' preferences for nodes. We theoretically prove that for any node-VN connectivity pattern, there exists a set of MAVN's parameters that can simulate the pattern. Experiments on nine real-world datasets demonstrate that MAVN consistently improves the performance of backbone MPNNs, achieving up to 46.5% improvement over the backbones and outperforms the baselines.

Problem

• Virtual Nodes
• Message Passing Neural Networks
• Dynamic Graph Representation
• Adaptive Connectivity
• Graph Neural Networks

Innovation

• Adaptive Virtual Nodes
• Dynamic Message Passing
• Graph Neural Networks
• Differentiable Architecture
• Node-VN Connectivity