2023/12/16 by Lidia Aceto, Aceto, Lidia, Pietro Antonio Grassi +1
Computer Science · Engineering · Physics and Astronomy · #37J06 #65L05 #65P99 #68T07 #70H33 #Artificial Intelligence (cs.AI) #Control and Stability of Dynamical Systems #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Machine Learning (cs.LG) #Mathematical Physics (math-ph) #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2312.10279
openalex publication_date 2023/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.