A charge-preserving method for solving graph neural diffusion networks
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Abstract (arXiv)
The aim of this paper is to give a systematic mathematical interpretation of the diffusion problem on which Graph Neural Networks (GNNs) models are based. The starting point of our approach is a dissipative functional leading to dynamical equations which allows us to study the symmetries of the model. We discuss the conserved charges and provide a charge-preserving numerical method for solving the dynamical equations. In any dynamical system and also in GRAph Neural Diffusion (GRAND), knowing the charge values and their conservation along the evolution flow could provide a way to understand how GNNs and other networks work with their learning capabilities.
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References · 14
- 2017Attention Is All You Needcited by 60,361
- 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
- 2019Hamiltonian Neural Networkscited by 712
- 2020Lagrangian Neural Networkscited by 398
- 2021GRAND: Graph Neural Diffusioncited by 258
- 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
- 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
- 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
- 2022Understanding convolution on graphs via energiescited by 59
- 2019Physical Symmetries Embedded in Neural Networkscited by 40
- 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
- 2022AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equationscited by 20
2 more
- 2019Learning Symmetries of Classical Integrable Systemscited by 15
- 2022Learning Linear Symmetries in Data Using Moment Matchingcited by 1
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