Simple and Deep Graph Convolutional Networks (2007.02133v1)

Abstract: Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .

Simple and Deep Graph Convolutional Networks

The paper "Simple and Deep Graph Convolutional Networks" by Ming Chen et al. addresses a persistent issue in the use of Graph Convolutional Networks (GCNs) for analyzing graph-structured data—the over-smoothing problem. Over-smoothing occurs when an increase in the number of GCN layers causes node representations to become indistinguishable, thereby degrading the model's performance. Most GCN models, including the well-known GCN by Kipf & Welling (2017) and GAT by Velickovic et al. (2018), achieve optimal performance with shallow architectures (typically 2 layers) due to this issue.

Key Contributions

To tackle this challenge, the authors propose a novel extension to the vanilla GCN model called GCNII (Graph Convolutional Network via Initial residual and Identity mapping). The main contributions of this paper are as follows:

1. GCNII Model: The GCNII model incorporates two techniques to mitigate over-smoothing: initial residual connections and identity mapping. Initial residual connections ensure that each layer retains information from the input layer, while identity mapping involves adding an identity matrix to the weight matrix of each layer. Together, these modifications allow the GCNII to support deeper network architectures.
2. Theoretical Analysis: The authors provide an in-depth theoretical analysis demonstrating that stacking k layers in the vanilla GCN essentially creates a fixed polynomial filter of order k, leading to over-smoothing. In contrast, a k-layer GCNII can express a polynomial filter of order k with arbitrary coefficients, significantly increasing its expressive power.
3. Empirical Performance: Through extensive experiments, the authors show that the deep GCNII model outperforms state-of-the-art methods on various semi-supervised and full-supervised tasks, demonstrating improved capability over several datasets.

Findings and Experimental Validation

The authors validate their hypotheses and models through a variety of empirical tests:

1. Semi-supervised Node Classification: GCNII achieved state-of-the-art performance on benchmark datasets such as Cora, Citeseer, and Pubmed. It consistently improved performance as the network depth increased, unlike other methods which either plateaued or declined due to over-smoothing.
2. Full-supervised Node Classification: GCNII outperformed other models on datasets such as Chameleon, Cornell, Texas, and Wisconsin. Notably, it provided a substantial performance gain on the Wisconsin dataset, emphasizing the benefits of adding non-linearity through identity mapping and initial residual connections.
3. Inductive Learning: On the Protein-Protein Interaction (PPI) dataset, GCNII set a new state-of-the-art performance, achieving higher micro-averaged F1 scores than previous methods. This showcases its capability to generalize well in inductive learning settings.

Implications and Future Directions

The implications of this work are multifaceted:

1. Model Depth: The introduction of initial residual connections and identity mapping techniques demonstrates that deeper GCNs can be effectively used without succumbing to over-smoothing, thus enabling better feature extraction from high-order neighbors in graph data.
2. Adaptive Filters: The ability of GCNII to express polynomial filters with arbitrary coefficients suggests potential improvements in capturing complex dependencies in graph data, which could be beneficial for tasks requiring deeper semantic understanding.
3. Generalization: The model's performance in inductive learning tasks indicates its robustness and suitability for practical applications needing generalization across different graph structures.

In future research, interesting directions include combining GCNII with attention mechanisms to possibly enhance its performance further, and analyzing the behavior of GCNII when varying the ReLU operation and other non-linearities.

In summary, the paper presents substantial advancements in the design and understanding of deep GCN architectures, providing both theoretical and empirical contributions that push the boundaries of what GCN models can achieve.