Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916612568776704 |
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| author | Heilig, Simon Gravina, Alessio Trenta, Alessandro Gallicchio, Claudio Bacciu, Davide |
| author_facet | Heilig, Simon Gravina, Alessio Trenta, Alessandro Gallicchio, Claudio Bacciu, Davide |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks Heilig, Simon Gravina, Alessio Trenta, Alessandro Gallicchio, Claudio Bacciu, Davide Machine Learning Systems and Control 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. |
| title | Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2405.17163 |