Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks

TL;DR

This paper introduces port-Hamiltonian Deep Graph Networks, a novel framework inspired by Hamiltonian systems, to improve long-range information propagation in graph neural networks, achieving state-of-the-art results.

Contribution

It presents a unified theoretical and practical framework combining non-dissipative and dissipative dynamics for graph neural networks, with guarantees on information conservation.

Findings

Achieves state-of-the-art performance on long-range graph benchmarks.

Provides theoretical guarantees on information conservation.

Applicable to general message-passing architectures.

Abstract

The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce (port-)Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.