{
  "id": "2405.17163",
  "version": "v2",
  "published": "2024-05-27T13:36:50.000Z",
  "updated": "2025-02-13T16:32:55.000Z",
  "title": "Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks",
  "authors": [
    "Simon Heilig",
    "Alessio Gravina",
    "Alessandro Trenta",
    "Claudio Gallicchio",
    "Davide Bacciu"
  ],
  "comment": "Accepted at ICLR 2025 (https://openreview.net/forum?id=03EkqSCKuO)",
  "categories": [
    "cs.LG",
    "cs.SY",
    "eess.SY"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-02-13T16:32:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep graph networks",
      "long-range propagation",
      "port-hamiltonian architectural bias",
      "simple graph convolutional architectures",
      "influences graph representation learning"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}