A charge-preserving method for solving graph neural diffusion networks

• URL: http://arxiv.org/abs/2312.10279v1
• Date: Sat, 16 Dec 2023 01:06:31 GMT
• Title: A charge-preserving method for solving graph neural diffusion networks
• Authors: Lidia Aceto and Pietro Antonio Grassi
• Abstract summary: This paper gives a systematic mathematical interpretation of the diffusion problem on which Graph Neural Networks (GNNs) models are based. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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