Zero-Shot Size Transfer for Neural ODEs on Sparse Random Graphs: Graphon Limits and Adjoint Convergence
arXiv:2606.26662v1 Announce Type: new Abstract: Graph Neural Differential Equations (GNDEs) model continuous-time graph dynamics by parameterizing Neural ODE velocity fields with Graph Neural Networks. Their local, size-independent filters suggest a zero-shot size-transfer principle: train on a small graph and deploy on larger, similar graphs without retraining. We develop a quantitative theory for this principle on sparse random graphs sampled from graphons. We consider Graphon Neural Differential Equations (Graphon-NDEs) and adjoint Graphon-NDEs as the infinite-node limits of the forward and
This research addresses a critical scalability challenge in neural networks, particularly pertinent as AI models grow ever larger and data sets more complex, making efficient deployment a key focus.
A strategic reader should care because zero-shot size transfer implies significant efficiency gains in AI deployment, reducing training costs and accelerating real-world application of complex graph-based AI systems.
The ability to train AI on small graphs and reliably deploy on larger ones without retraining fundamentally alters the economic and operational model for developing and scaling AI solutions for network-structured data.
- · AI developers
- · Cloud computing providers (reduced egress/compute for retraining)
- · Industries with large, dynamic networks (e.g., logistics, telecom, social media)
- · Hardware manufacturers (more efficient utilization of existing silicon)
- · Inefficient AI training model developers
- · Sectors reliant on constant retraining for new data topologies
Reduced computational costs and time for deploying neural ordinary differential equations on larger graph structures.
Accelerated adoption of graph neural networks in applications requiring real-time adaptation to evolving network sizes, such as cybersecurity or dynamic supply chain optimization.
Democratization of advanced AI for complex systems, lowering barriers for smaller entities to deploy sophisticated graph-based models without immense computational resources for retraining.
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Read at arXiv cs.LG