arXiv:2605.31315v1 Announce Type: new Abstract: We show that contrary to conventional wisdom in the community, graph neural networks (GNNs) are not continuous with respect to all natural modes of graph convergence. As a result, GNNs may generate substantially different latent representations for graphs that are very similar. In particular they assign vastly different latent embeddings to graphs that represent the same underlying object at different resolution scales. We trace this failure of continuity back to a structural obstruction arising from commonly used information-propagation schemes.
This research emerges as GNNs become increasingly central to various AI applications, prompting deeper scrutiny into their fundamental limitations as they scale.
A strategic reader should care because this discovery challenges a core assumption about GNN robustness and highlights a fundamental limitation that could impact AI model reliability and generalization.
The understanding that GNNs are not inherently continuous across graph resolutions changes how these models should be designed, evaluated, and applied, particularly in tasks involving multi-scale data.
- · Researchers developing novel neural network architectures
- · Developers of robust graph pre-processing techniques
- · Industries requiring high-assurance AI systems
- · Developers relying solely on conventional GNN architectures for multi-resolution
- · Applications where subtle graph changes lead to critical decision shifts
- · GNN models deployed without rigorous assessment of continuity
The finding necessitates a re-evaluation of current GNN designs and potential modifications to achieve resolution invariance.
This could lead to a bifurcation of GNN research into robust, resolution-invariant models and those where this limitation is explicitly managed or accepted.
New benchmarks and theoretical frameworks may emerge to specifically test and quantify GNN continuity and robustness across different graph representations.
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Read at arXiv cs.LG