A charge-preserving method for solving graph neural diffusion networks
This provides a systematic interpretation for understanding GNN learning capabilities, but it appears incremental as it builds on existing GRAND models without claiming broad SOTA gains.
The paper tackles the problem of interpreting diffusion in Graph Neural Networks (GNNs) by developing a mathematical framework based on dissipative functionals and dynamical equations, resulting in a charge-preserving numerical method for solving these equations.
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.