Structure-Aware Transformer for Graph Representation Learning (2202.03036v3)

Abstract: The Transformer architecture has gained growing attention in graph representation learning recently, as it naturally overcomes several limitations of graph neural networks (GNNs) by avoiding their strict structural inductive biases and instead only encoding the graph structure via positional encoding. Here, we show that the node representations generated by the Transformer with positional encoding do not necessarily capture structural similarity between them. To address this issue, we propose the Structure-Aware Transformer, a class of simple and flexible graph Transformers built upon a new self-attention mechanism. This new self-attention incorporates structural information into the original self-attention by extracting a subgraph representation rooted at each node before computing the attention. We propose several methods for automatically generating the subgraph representation and show theoretically that the resulting representations are at least as expressive as the subgraph representations. Empirically, our method achieves state-of-the-art performance on five graph prediction benchmarks. Our structure-aware framework can leverage any existing GNN to extract the subgraph representation, and we show that it systematically improves performance relative to the base GNN model, successfully combining the advantages of GNNs and Transformers. Our code is available at https://github.com/BorgwardtLab/SAT.

Overview of Structure-Aware Transformers in Node Classification

The paper presents a novel approach in the domain of graph neural networks by introducing Structure-Aware Transformers (SAT) specifically designed for node classification tasks. SAT diverges from the standard Transformer with random walk positional encodings (RWPE) by integrating structure-aware node embeddings that significantly enhance performance on certain datasets, as demonstrated with case studies like Mutagenicity. The SAT model's design aims to leverage graph structural information without incurring the substantial computational costs typical of traditional transformers when scaling to larger datasets.

Key Contributions and Results

The primary contribution of the paper is the development of the SAT model, which utilizes structure-aware node embeddings, enhancing model focus on domain-relevant motifs within graphs. The model is tested on datasets known for specific structural motifs, such as the Mutagenicity dataset, where SAT achieved a prediction accuracy of 82%, compared to 78% for a Transformer utilizing only RWPE. This distinction emphasizes the potential of SAT's structure-focused attention mechanism over traditional position-based methods.

The paper includes promising experimental results across node classification tasks, indicating SAT's robust prediction accuracy. Notably, SAT is evaluated on datasets like PATTERN and CLUSTER, despite challenges related to the computational complexity in processing large graphs. SAT's architecture, enhanced through a scalable k-subtree GNN-based structure extractor, allows it to generalize node representations without explicitly extracting subgraphs.

Methodological Insights

SAT is structured to encode graph topology through structure-aware node representations, utilizing them as queries and keys in the self-attention mechanism. The paper articulates the differences between SAT and existing Subgraph Neural Networks (SNN), clarifying that SAT focuses on the structural interactions between nodes at each layer, rather than relying on explicit subgraph delineations.

The paper also touches on the incorporation of edge attributes in the SAT model. While the attentional mechanism of SAT does not utilize edge attributes directly, these attributes are factored in through the GNN structure extractor. However, these attributes remain static across layers, hinting at a potential area for future research enhancements.

Implications and Future Research

The paper extends its discussion to the consideration of various positional encoding strategies, conducting novel experiments with permuted and random encodings to isolate the effects of positional encodings within graph data. These experimental insights could inspire further exploration of positional encoding's role in graph-based learning methods.

Practically, the development of efficient transformers and advanced node sampling strategies are suggested as promising areas for further research to overcome current limitations regarding SAT's scalability with large-scale graphs, such as ogbn-products. Additionally, integrating aspects of SNN into new structure extractors within the SAT framework could yield further empirical and theoretical advancements.

In conclusion, this paper offers substantial progress in enhancing transformer models' capabilities by incorporating structure-awareness for node classification tasks. While demonstrating notable success with specific graph datasets, it also opens numerous avenues for future inquiry, particularly in addressing scalability concerns and enriching model architecture with more complex network features.