Revisiting Graph Neural Networks: All We Have is Low-Pass Filters
This work provides foundational insights for researchers in graph machine learning, revealing that GNNs may be less powerful than assumed, which is incremental but clarifies theoretical bottlenecks.
The paper tackles the problem of understanding the limitations of graph neural networks (GNNs) by analyzing their theoretical properties, finding that they only perform low-pass filtering on features and lack non-linear manifold learning, with results showing that graph structure primarily denoises data in benchmark datasets.
Graph neural networks have become one of the most important techniques to solve machine learning problems on graph-structured data. Recent work on vertex classification proposed deep and distributed learning models to achieve high performance and scalability. However, we find that the feature vectors of benchmark datasets are already quite informative for the classification task, and the graph structure only provides a means to denoise the data. In this paper, we develop a theoretical framework based on graph signal processing for analyzing graph neural networks. Our results indicate that graph neural networks only perform low-pass filtering on feature vectors and do not have the non-linear manifold learning property. We further investigate their resilience to feature noise and propose some insights on GCN-based graph neural network design.