Title: Boltzmann Graph Networks: Efficient Energy-Based Framework for Graph Representation Learning
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Neural Networks, Energy-Based Learning, Restricted Boltzmann Machines, Node Representation Learning

Abstract: With the rapid growth of interconnected data, graph-structured representations have become essential for modeling complex relational systems. Graph Neural Networks (GNNs) are widely used architectures for leveraging semantic information encoded in nodes and edges. The current GNN models encounter multiple challenges, including over-smoothing along with restricted ability to model distant dependencies and excessive computational requirements from complex graph structures. This paper introduces Boltzmann Graph Network (BGN), a novel and efficient GNN architecture that integrates energy-based probabilistic models with deterministic graph convolution techniques. By conceptualizing the graph as an energy landscape, BGN employs a Boltzmann-inspired energy function to capture intricate node and edge interactions, enabling robust representation learning. The use of k-step persistent contrastive divergence while ensuring compatibility with gradient-based optimization, mitigates over-smoothing, and enhances long-range dependency modeling. Comprehensive evaluations for node prediction on citation network benchmarks show that BGN achieves state-of-the-art performance on both random and Geom-GCN splits. With test accuracies of 88.0% (Cora), 75.6% (CiteSeer), and 85.6% (PubMed) on random splits, while on Geom-GCN splits the model attains 85.8% (Cora), 75.5% (CiteSeer), and 88.2% (PubMed), demonstrating consistent improvements over existing methods. These results highlight BGN’s scalability, robustness, and efficiency, positioning it as a powerful framework for advancing graph-based learning across diverse applications.

TL;DR: Boltzmann Graph Networks (BGNs) introduce an efficient, energy-based GNN for robust node representation learning in citation network node classification.