Investigating Zero-Shot Size Transfer of Graph Neural Differential Equations for Learning Graph Diffusion Dynamics

Charles Kulick, Björn Birnir, Sui Tang

Track: Extended Abstract (non-archival, 4 pages)

Keywords: Neural ODEs, Graphs, Graphons, Size Transfer

Abstract: Graph Neural Differential Equations (GNDEs) provide a powerful framework for learning continuous-time dynamics on discrete graphs. A key advantage of GNDEs is their potential to transfer learned parameters from small training graphs to much larger test graphs. While recent theory establishes convergence guarantees for this size transfer, its practical behavior in trained models remains unclear. In this work, we empirically investigate the zero-shot size transferability of GNDEs for learning graph diffusion dynamics that admit a graphon limit, and reveal how transfer accuracy depends on the underlying dynamics and graph structure. In particular, we observe a clear convergence rate when fitting GNDEs to linear diffusion dynamics across graph sizes, a phenomenon absent in nonlinear settings, raising new theoretical questions about the mechanisms underlying transfer learning.

Submission Number: 37