Graph Neural Networks Need Cluster-Normalize-Activate Modules (2412.04064v1)

Abstract: Graph Neural Networks (GNNs) are non-Euclidean deep learning models for graph-structured data. Despite their successful and diverse applications, oversmoothing prohibits deep architectures due to node features converging to a single fixed point. This severely limits their potential to solve complex tasks. To counteract this tendency, we propose a plug-and-play module consisting of three steps: Cluster-Normalize-Activate (CNA). By applying CNA modules, GNNs search and form super nodes in each layer, which are normalized and activated individually. We demonstrate in node classification and property prediction tasks that CNA significantly improves the accuracy over the state-of-the-art. Particularly, CNA reaches 94.18% and 95.75% accuracy on Cora and CiteSeer, respectively. It further benefits GNNs in regression tasks as well, reducing the mean squared error compared to all baselines. At the same time, GNNs with CNA require substantially fewer learnable parameters than competing architectures.

• The paper introduces Cluster-Normalize-Activate (CNA) modules with Cluster, Normalize, and Activate stages as a plug-and-play method to mitigate oversmoothing and enhance GNN expressivity.
• Empirical evaluation shows CNA-enhanced GNNs achieve state-of-the-art performance, including 94.18% classification accuracy on Cora and reduced NMSE on regression tasks, across various architectures and datasets.
• The study demonstrates CNA's potential for enabling deeper GNN architectures while maintaining feature distinctiveness and promoting parameter efficiency for large-scale applications.

Analyzing the Implications of Cluster-Normalize-Activate Modules in Graph Neural Networks

Graph Neural Networks (GNNs) have proven to be a significant tool in handling structured data across various domains, including molecular stability prediction and social network analysis. However, their utility is often constrained by a phenomenon called oversmoothing. In their paper, Skryagin et al. propose an innovative solution through Cluster-Normalize-Activate (CNA) modules to attenuate this challenge and enhance GNN expressivity.

Key Contributions and Methodology

The core proposal of the paper is the introduction of CNA modules as a plug-and-play component to mitigate oversmoothing in GNNs. The methodology consists of three pivotal stages:

1. Cluster: Node features are grouped into clusters, which serve as super-nodes. This step is shown to discern shared and distinct properties effectively without altering the graph's original topology.
2. Normalize: Within each cluster, node features are normalized separately to stabilize training, similar to practices seen in other deep learning disciplines, such as Transformers.
3. Activate: Unlike typical affine transformations, learnable activation functions specific to each cluster are employed. Rational activation functions, known for their flexibility, are utilized to empower the transformations.

The CNA modules can theoretically improve the distinction among node representations even in deeper networks, making them more robust against oversmoothing. This is particularly relevant as the depth of GNNs has been a limiting factor due to convergence of features leading to indistinguishable node representations.

Empirical Evaluation

Experiments underscore CNA's efficacy across multiple datasets and tasks. Notably, CNA-enhanced GNN architectures achieve remarkable classification accuracies of 94.18% and 95.75% on the Cora and CiteSeer datasets, respectively, surpassing several state-of-the-art benchmarks. These robust improvements are consistent across a variety of architectures including Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), and GraphSAGE, implying significant versatility.

Further assessment on node regression tasks with multi-scale node regression datasets like Chameleon and Squirrel demonstrates CNA's superiority in reducing normalized mean squared error (NMSE), suggesting better predictive performance in complex real-world scenarios.

Theoretical and Practical Implications

The paper challenges existing theoretical proofs regarding the inevitability of oversmoothing by demonstrating that CNA's design principles can diverge from traditional assumptions. Consequently, this innovates a pathway for deeper GNN architectures that maintain feature distinctiveness.

From a practical standpoint, CNA modules promote parameter parsimony. With fewer parameters, models equipped with CNA achieve competitive performance, thereby reducing the computational load and opening avenues for scaling up GNNs in large-scale applications.

Future Directions

The authors shed light on several promising directions for future research. Firstly, exploring other clustering algorithms that may yield better or more efficient clustering performance can be valuable. Secondly, augmenting CNA with complementary methodologies like Edge Dropout or Global Pooling could offer additive improvements. Additionally, the paper hints at extending the CNA concept beyond GNNs to Transformer architectures, drawing connections between clustering-based normalization and expressivity improvements.

In conclusion, the introduction of CNA modules represents a meaningful stride in addressing GNN limitations, facilitating deeper architectures while enhancing performance and efficiency. This work stands to catalyze further innovations in graph learning, with strong implications for real-world applicability across complex structured data tasks.