Injecting Hamiltonian Architectural Bias into Deep Graph Networks for Long-Range Propagation
<|reference_start|>Injecting Hamiltonian Architectural Bias into Deep Graph Networks for Long-Range Propagation: 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.<|reference_end|>
@article{heilig2024injecting,
    title={Injecting Hamiltonian Architectural Bias into Deep Graph Networks for
  Long-Range Propagation},
    author={Simon Heilig, Alessio Gravina, Alessandro Trenta, Claudio Gallicchio,
  Davide Bacciu},
    journal={arXiv preprint arXiv:2405.17163},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.17163},
    primaryClass={cs.LG cs.SY eess.SY}
}