Do Higher-Order Models Win for Higher-Order Reasons? Rethinking Performance Gains in Hypergraph Learning

2026-10-06

AI Summary

This study addresses whether the performance advantages of hypergraph learning models genuinely stem from higher-order information. To rectify this attribution bias, we propose a controlled attribution framework that perturbs higher-order structures while preserving lower-order topology, systematically evaluating the true sources of performance gains across 25 benchmarks. Our findings reveal that the superiority of most hypergraph models can be explained by lower-order mechanisms without relying on higher-order information. This work establishes a new paradigm for disentangling performance gains from their underlying causes and exposes baseline deficiencies in existing evaluations. Consequently, we call upon the research community to adopt stronger lower-order baselines and more rigorous benchmarks for comparative analysis.

Abstract

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. 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. 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. 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.

Problem

• hypergraph learning
• higher-order models
• performance attribution
• higher-order information

Innovation

• Hypergraph Learning
• Higher-Order Models
• Performance Attribution
• Controlled Perturbation Framework
• Lower-Order Baselines