Beyond smoothness: A general optimization framework for graph neural networks with negative Laplacian regularization.

Area of Science:

• Machine Learning
• Graph Neural Networks
• Data Science

Background:

• Graph Neural Networks (GNNs) are effective for graph-structured data.
• Existing GNN frameworks often model graph convolution as signal denoising, which struggles with heterophilic graphs and leads to shallow models by prioritizing feature smoothness.
• This smoothness constraint overlooks crucial high-frequency information in node features.

Purpose of the Study:

• To propose a general framework for GNNs that overcomes the limitations of smoothness-regularized approaches.
• To develop a more flexible graph convolution operator capable of learning both low- and high-frequency components adaptively.
• To enhance GNN performance, particularly on heterophilic graphs, and enable deeper architectures.

Main Methods:

• Introduced a novel GNN framework by relaxing smoothness regularization.
• Employed an adaptive information aggregation mechanism to learn low- and high-frequency feature components.
• Conducted theoretical analyses to validate the framework's ability to capture diverse frequency information.

Main Results:

• The proposed framework effectively captures both low- and high-frequency information in node features.
• Achieved state-of-the-art performance on nine benchmark datasets.
• Demonstrated the framework's capability to support deeper GNN models and resist adversarial attacks.

Conclusions:

• The new GNN framework offers a more flexible and powerful approach to graph representation learning.
• By adaptively learning frequency components, the framework significantly improves performance, especially on challenging heterophilic graphs.
• This work paves the way for more robust, interpretable, and capable deep GNN models.