Revisiting Graph Neural Networks: All We Have is Low-Pass Filters (1905.09550v2)

Abstract: 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.

• The paper demonstrates that GNNs primarily act as low-pass filters, suggesting that simplified models can achieve competitive performance on benchmark datasets.
• A graph signal processing framework reveals that low-frequency components carry most of the predictive signal, questioning the need for complex non-linear layers.
• Experimental findings indicate that when features are low-frequency dominant, efficient models like gfNN can outperform conventional GCNs in noise reduction and performance.

Revisiting Graph Neural Networks: All We Have is Low-Pass Filters

The paper "Revisiting Graph Neural Networks: All We Have is Low-Pass Filters" provides a rigorous theoretical exploration of the operations underpinning Graph Neural Networks (GNNs), fundamentally questioning the necessity of their complex architectures designed for learning on graph-structured data. The authors scrutinize the widely held perception that GNNs owe their effectiveness to sophisticated learning mechanisms akin to non-linear manifold learning.

Core Claims and Methodology

At the center of this work is the assertion that GNNs, including Graph Convolutional Networks (GCNs), predominantly perform low-pass filtering on input features rather than engaging in the non-linear manifold learning presumed in broader neural networks. This claim is investigated by framing GNN operations within the context of graph signal processing (GSP).

The paper proceeds to validate its hypothesis through several key contributions:

1. Dataset Feature Analysis: Using well-regarded benchmark datasets like Cora, Citeseer, and Pubmed, the authors demonstrate that low-frequency components of feature vectors carry most of the predictive signal. Their experiments show that upon the removal of high-frequency noise from features, a simpler model such as a multi-layer perceptron (MLP) performs comparably well.
2. Theoretical Framework: A graph signal processing approach is employed to provide evidence that multiplying feature vectors by graph adjacency matrices acts as low-pass filtering. This operation effectively emphasizes low-frequency components and dampens higher frequencies that are largely irrelevant or noise.
3. Model Implications: By comparing the outcomes of MLPs with those of GCNs and proposing an alternative model, the graph filter neural network (gfNN), the paper highlights conditions under which complex GNN architectures might not be necessary. The paper theoretically posits that, assuming meaningful features exhibit low-frequency characteristics, simpler linear transformations followed by basic neural network layers suffice.

Experimental Findings

Experiments on synthetic data further elucidate situations where current GNN models like Simple Graph Convolution (SGC) can fail—particularly in non-linear feature spaces that cannot be simplified or denoised effectively through low-pass filtering alone. Their experiments display GCN's limitations in handling noisy inputs and emphasize gfNN’s resilience through efficient denoising.

Implications and Future Directions

The insights from this paper invite a reevaluation of how GNNs are designed and deployed across various domains. Given that many GNNs provide similar results due to information already being embedded in low-frequency feature components, the emphasis on complex GCN layers becomes questionable, particularly when computational efficiency and noise resilience are prioritized.

The implications extend to practical applications in fields such as biology and social networks analysis, where GNNs are widely used. By advocating for simplified architectures like gfNN, the authors propose cost-effective models that only use graph filters where truly beneficial.

Future research is encouraged to explore novel architectures that adjust dynamically to the frequency distribution of input graphs, ensuring robust performance even when high-frequency components contribute valuable information—a scenario not covered under the current low-pass filtering framework.

In conclusion, the paper delivers a compelling argument that compels practitioners to consider when graph structure is genuinely suitable for enhancing feature representations and when it may merely act as a computational detour achieving little beyond feature noise reduction.