Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily

TL;DR

This work addresses node classification on graphs with varying homophily levels, where fixed-depth GNNs underperform. It develops a node-level theoretical framework linking local neighborhood label distribution to optimal propagation depth and introduces AD-GNN, an architecture that assigns per-node aggregation depth via a depth-benefit metric and a stopping rule. A fast variant, AD-GNN_fast, uses degree-based similarity to reduce cost while preserving performance. Extensive experiments across homophilic and heterophilic benchmarks show consistent gains for standard backbones and demonstrate reduced oversmoothing with adaptive depth, highlighting practical impact for robust node representations across diverse graphs.

Abstract

Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels or properties. While recent work has introduced mechanisms to improve GNN performance under heterophily, certain key limitations still exist. Most existing models apply a fixed aggregation depth across all nodes, overlooking the fact that nodes may require different propagation depths based on their local homophily levels and neighborhood structures. Moreover, many methods are tailored to either homophilic or heterophilic settings, lacking the flexibility to generalize across both regimes. To address these challenges, we develop a theoretical framework that links local structural and label characteristics to information propagation dynamics at the node level. Our analysis shows that optimal aggregation depth varies across nodes and is critical for preserving class-discriminative information. Guided by this insight, we propose a novel adaptive-depth GNN architecture that dynamically selects node-specific aggregation depths using theoretically grounded metrics. Our method seamlessly adapts to both homophilic and heterophilic patterns within a unified model. Extensive experiments demonstrate that our approach consistently enhances the performance of standard GNN backbones across diverse benchmarks.

Figures (14)

• Figure 1: High-level workflow of AD-GNN: First, the depth benefit metric for each node is computed using their node profile and learned label probabilities. Then, the depth for each node is determined based on a learnable threshold mechanism. Nodes that have higher depth benefit metrics will receive more aggregation layers compared to others.
• Figure 5: Degree distribution of datasets.
• Figure 6: Layer-wise Embedding Visualization for Citeseer Dataset. Sil and CH acronyms refer to the silhouette score and the Calinski-Harabasz score, respectively.
• Figure 7: Runtime (per epoch) comparison between different heuristics.
• Figure 8: Average depth benefit metric computed per degree in homophilic and heterophilic datasets.

Theorems & Definitions (19)

• Definition 1: Class Concepts
• Definition 2: Label-Based Aggregation
• Definition 3: Signal Preservation Factor
• Theorem 1: Label Aggregation Effect
• Corollary 1: Strong Homophily
• Corollary 2: Strong Heterophily
• Corollary 3: Mixed Homophily/Heterophily
• Theorem 2: Iterative Aggregation Effect
• Remark 1
• Definition 4: Depth Benefit Metric