Decoupling the Depth and Scope of Graph Neural Networks (2201.07858v1)

Abstract: State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond just a few layers, two fundamental challenges emerge: 1. degraded expressivity due to oversmoothing, and 2. expensive computation due to neighborhood explosion. We propose a design principle to decouple the depth and scope of GNNs -- to generate representation of a target entity (i.e., a node or an edge), we first extract a localized subgraph as the bounded-size scope, and then apply a GNN of arbitrary depth on top of the subgraph. A properly extracted subgraph consists of a small number of critical neighbors, while excluding irrelevant ones. The GNN, no matter how deep it is, smooths the local neighborhood into informative representation rather than oversmoothing the global graph into "white noise". Theoretically, decoupling improves the GNN expressive power from the perspectives of graph signal processing (GCN), function approximation (GraphSAGE) and topological learning (GIN). Empirically, on seven graphs (with up to 110M nodes) and six backbone GNN architectures, our design achieves significant accuracy improvement with orders of magnitude reduction in computation and hardware cost.

• The paper introduces a decoupling principle that separates GNN depth from scope to mitigate oversmoothing and reduce computational costs.
• It leverages subgraph extraction methods, including Personalized PageRank, to enable deep architectures with focused local information.
• Empirical results on datasets with up to 110M nodes show significant accuracy improvements and reduced hardware requirements.

Decoupling Depth and Scope in Graph Neural Networks

The paper "Decoupling the Depth and Scope of Graph Neural Networks" addresses the scalability and expressivity challenges faced by Graph Neural Networks (GNNs) when applied to large-scale graphs. The research introduces a novel design principle that decouples the depth and scope of GNN models, thus offering a new dimension in GNN design space which improves both scalability and expressivity without modifying existing architectural components.

Challenges and Motivation

As GNNs gain prominence in various applications such as recommendation systems, knowledge graph understanding, and drug discovery, their scalability and expressivity issues become critical. One major challenge is oversmoothing, where increasing the number of GNN layers causes node embeddings to converge into indistinguishable representations. Another issue is the high computational cost associated with the neighborhood explosion problem, where multi-hop expansion dramatically increases the receptive field and computation requirements.

Most current solutions involve architectural modifications or sampling techniques which only partially address these problems. The paper proposes an alternative approach by reinterpreting graph data to separate the global and local views, allowing for a decoupled consideration of the depth of GNN layers and the scope of the subgraphs these layers operate upon.

Proposed Solution and Methodology

The authors propose a framework where GNN depth and scope are decoupled, allowing GNNs to be deeper while maintaining a constrained scope. The decoupling is achieved by extracting a subgraph around each target node, which captures the most relevant local information. The GNN model, which can now be of arbitrary depth, operates on these smaller subgraphs. This design leverages the benefits of deep GNN models while mitigating oversmoothing and computational inefficiencies.

The proposed approach is demonstrated using a practical implementation known as SHA D OW -GNN, where the subgraphs comprise of nodes within two or three hops. Various subgraph extraction techniques are explored, such as the Personalized PageRank (PPR)-based extraction, which considers node importance relative to the target node.

Theoretical Perspectives and Empirical Validation

The paper provides detailed theoretical analysis from multiple perspectives, including graph signal processing, function approximation, and topological learning. It shows, via theoretical proofs, that the decoupled approach preserves local feature and structural information, prevents oversmoothing, reduces approximation error, and makes the model more discriminative than traditional GNNs.

Empirically, the SHA D OW -GNN model was tested on seven datasets, involving up to 110 million nodes, across different GNN architectures. The results demonstrate significant improvements in accuracy and computational efficiency, with orders of magnitude reduction in inference and hardware costs compared to traditional approaches. For instance, in tasks such as node classification on large-scale graphs, SHA D OW -GNN achieved notable accuracy improvements with much lower computational burden.

Implications and Future Directions

The decoupling principle introduced in this work has significant implications for scaling up GNNs without sacrificing expressivity. The ability to treat depth and scope as independent parameters opens opportunities to explore deeper GNN architectures while maintaining computational feasibility. Furthermore, as graph data continues to grow in size and complexity, the proposed framework provides a viable pathway to deploy GNNs in real-world applications with large and dynamic graphs.

Future exploration could focus on refining subgraph extraction methods, integrating learning-based approaches, and further enhancing the scalability of decoupled models. Moreover, examining more diverse tasks, including link prediction and beyond, could further validate the versatility and robustness of the proposed approach. The potential to integrate this decoupling principle into existing GNN frameworks and beyond promises to advance the development of more efficient, scalable, and expressive graph-based models.