Exploring Heterophily in Graph-level Tasks

While heterophily has been widely studied in node-level tasks, its impact on graph-level tasks remains unclear. We present the first analysis of heterophily in graph-level learning, combining theoretical insights with empirical validation. We first introduce a taxonomy of graph-level labeling schemes, and focus on motif-based tasks within local structure labeling, which is a popular labeling scheme. Using energy-based gradient flow analysis, we reveal a key insight: unlike frequency-dominated regimes in node-level tasks, motif detection requires mixed-frequency dynamics to remain flexible across multiple spectral components. Our theory shows that motif objectives are inherently misaligned with global frequency dominance, demanding distinct architectural considerations. Experiments on synthetic datasets with controlled heterophily and real-world molecular property prediction support our findings, showing that frequency-adaptive model outperform frequency-dominated models. This work establishes a new theoretical understanding of heterophily in graph-level learning and offers guidance for designing effective GNN architectures.