Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment
This work provides a critical refinement for researchers applying hyperbolic embeddings, highlighting that task alignment is as important as graph structure, which is incremental but clarifies a key condition for effectiveness.
The authors investigated whether hyperbolic graph neural networks (HGNNs) are effective only when the task aligns with hyperbolic geometry, showing that HGNNs outperform Euclidean models in geometry-aligned tasks like link prediction but not in others like node classification.
Many complex networks exhibit hyperbolic structural properties, making hyperbolic space a natural candidate for representing hierarchical and tree-like graphs with low distortion. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely adopted as a principled choice for representation learning on tree-like graphs. In this work, we question this paradigm by proposing an additional condition of geometry-task alignment, i.e., whether the metric structure of the target follows that of the input graph. We theoretically and empirically demonstrate the capability of HGNNs to recover low-distortion representations on two synthetic regression problems, and show that their geometric inductive bias becomes helpful when the problem requires preserving metric structure. Additionally, we evaluate HGNNs on the tasks of link prediction and node classification by jointly analyzing predictive performance and embedding distortion, revealing that only link prediction is geometry-aligned. Overall, our findings shift the focus from only asking "Is the graph hyperbolic?" to also questioning "Is the task aligned with hyperbolic geometry?", showing that HGNNs consistently outperform Euclidean models under such alignment, while their advantage vanishes otherwise.