Yes, the manifold-based perspective can provide valuable insights into the transferability of GNNs across different domains or tasks. The theoretical framework established in the paper highlights how GNNs can generalize from one set of sampled points (or graphs) to unseen points within the same manifold. This principle can be extended to understand transferability across different domains by considering the following aspects:
Shared Manifold Structures: If different domains or tasks can be represented as different manifolds with similar geometric properties, the insights gained from one domain can be leveraged in another. For example, if two biological networks exhibit similar topological structures, a GNN trained on one network may effectively transfer its learned representations to the other, provided that the underlying manifold characteristics are comparable.
Domain Adaptation: The manifold perspective can inform domain adaptation strategies by identifying the commonalities in the manifold structures of different tasks. Techniques such as manifold alignment can be employed to align the learned representations from one domain to another, enhancing the GNN's ability to generalize across tasks.
Task Similarity: The analysis suggests that the generalization capabilities of GNNs are influenced by the complexity of the underlying manifold. Therefore, tasks that share similar manifold complexities may benefit from knowledge transfer. For instance, a GNN trained for node classification in one social network may be adapted for another social network with similar structural properties, improving performance without extensive retraining.
In summary, the manifold-based perspective not only enhances our understanding of GNN generalization but also provides a framework for improving the design, tuning, and transferability of GNNs across various applications and domains.