Understanding the Generalization Performance of GNNs: Topology Awareness and Future Directions

Table of Links

Abstract and 1 Introduction

2 Related Work

3 Framework

4 Main Results

5 A Case Study on Shortest-Path Distance

6 Conclusion and Discussion, and References

7 Proof of Theorem 1

8 Proof of Theorem 2

9 Procedure for Solving Eq. (6)

10 Additional Experiments Details and Results

11 Other Potential Applications

6 Conclusion and Discussion

In this work, we study and investigate GNNs which are fundamental to many computer vision and machine learning tasks. In particular, we explore the relationship between the topology awareness and generalization performance of GNNs. We introduce a novel framework that connects the structural awareness of GNNs with approximate metric embedding, offering a fresh perspective on their generalization capabilities in semi-supervised node classification tasks. This structure-agnostic framework facilitates a deeper, more intuitive comprehension of GNN generalizability across varied graph structures. Through a case study centered on graph distance, we demonstrate that our theoretical findings regarding structural results are reflected in the practical generalization performance of GNNs. Additionally, our findings shed light on the cold start problem in graph active learning and could influence various significant GNN applications.

6.1 Limitation and Future Works

Our proposed framework introduces a novel angle on GNN generalization performance, yet it is not without limitations. The current approach interprets GNN embeddings in terms of metric mapping and describes the structure awareness of GNNs through distortion. This perspective, however, overlooks the specific dynamics that contribute to reduced distortion within GNNs. Investigating these underlying dynamics would significantly enrich this area of research. Moreover, our study primarily examines the transductive setting. Expanding this analysis to the inductive setting—where the model is trained on one graph but applied to another—would offer a more comprehensive view of GNN generalization capabilities.

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