Higher-order models (e.g., hypergraph neural networks) often outperform lower-order baselines on hypergraph learning benchmarks, and their advantages are commonly attributed to their ability to exploit higher-order information.
However, better performance alone does not establish this explanation. We therefore ask: Do higher-order models win for higher-order reasons?
To investigate this question, we introduce a controlled performance-attribution framework that perturbs higher-order information while preserving the lower-order, i.e., pairwise, information.
Experiments and Observations
Across 25 commonly used hypergraph learning benchmarks spanning three tasks, we frequently observe an intriguing pattern:
higher-order models originally outperform lower-order baselines, yet retain most of their advantage after perturbation.
This suggests that much of the observed advantage remains achievable without the higher-order information.
Lower-order Explanations
We then investigate potential lower-order explanations for these remaining gaps.
We find that simple additions to a lower-order baseline, e.g., richer pairwise weighting, more steps of pairwise feature propagation, and normalization, reduce the remaining performance gaps, supporting lower-order explanations for part of the observed advantage.
Conclusion and Recommendations
Our analysis calls for the hypergraph learning community to rethink performance attribution by distinguishing performance gains from their explanations, adopt stronger lower-order baselines, and use suitable benchmarks that better test the value of higher-order information.