The insights from the theoretical analysis of NBA-GNN's expressive power can be instrumental in designing new GNN models tailored for specific application domains. For instance, the findings regarding the sensitivity bounds and over-squashing effects can guide the development of GNNs that are particularly effective in domains requiring high sensitivity to node features, such as social network analysis or fraud detection. By leveraging the non-backtracking property, new models can be designed to ensure that critical information from distant nodes is preserved and effectively utilized.
In domains like bioinformatics, where the structure of molecular graphs is crucial, the ability of NBA-GNN to recover hidden structures in sparse graphs can be harnessed to create specialized models that excel in predicting molecular properties or interactions. This could involve integrating domain-specific knowledge into the model architecture, such as incorporating chemical bonding rules into the non-backtracking message-passing framework.
Furthermore, the theoretical insights can inform the design of GNNs that are robust to noise and outliers, which is particularly relevant in real-world applications such as sensor networks or financial transaction graphs. By understanding how non-backtracking updates influence the model's expressiveness, researchers can create GNNs that maintain performance even in the presence of noisy data, thereby enhancing their applicability across various domains.