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

arXiv: https://arxiv.org/abs/2405.17163 · HTML: https://mlsanity.com/paper/2405.17163/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2024.

## Built on by (most cited first, 16 of 16)

- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks](https://mlsanity.com/paper/2506.07624/) (2025)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [Can You Hear Me Now? A Benchmark for Long-Range Graph Propagation](https://mlsanity.com/paper/2512.17762/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [Early-Exit Graph Neural Networks](https://mlsanity.com/paper/2505.18088/) (2025)
- [Stochastic Parroting in Temporal Attention -- Regulating the Diagonal Sink](https://mlsanity.com/paper/2602.10956/) (2026)
- [TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows](https://mlsanity.com/paper/2508.05070/) (2025)
- [gLSTM: Mitigating Over-Squashing by Increasing Storage Capacity](https://mlsanity.com/paper/2510.08450/) (2025)
- [From Message-Passing to Linearized Graph Sequence Models](https://mlsanity.com/paper/2605.12358/) (2026)
- [Information propagation dynamics in Deep Graph Networks](https://mlsanity.com/paper/2410.10464/) (2024)
- [Non-Dissipative Graph Propagation for Non-Local Community Detection](https://mlsanity.com/paper/2508.14097/) (2025)
- [TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks](https://mlsanity.com/paper/2609.32940/) (2026)
- [Reachability is not enough: Diagnosing long-range behavior in GNNs](https://mlsanity.com/paper/2609.33674/) (2026)
- [Get a GRIP, this will be a long TRIP: A Quantifiable Long-Range Framework for Verifying Over-squashing](https://mlsanity.com/paper/2610.03556/) (2026)
- [Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective](https://mlsanity.com/paper/2610.04157/) (2026)

## Abstract (arXiv)

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.