AnchorGT: Efficient and Flexible Attention Architecture for Scalable Graph Transformers (2405.03481v1)

Abstract: Graph Transformers (GTs) have significantly advanced the field of graph representation learning by overcoming the limitations of message-passing graph neural networks (GNNs) and demonstrating promising performance and expressive power. However, the quadratic complexity of self-attention mechanism in GTs has limited their scalability, and previous approaches to address this issue often suffer from expressiveness degradation or lack of versatility. To address this issue, we propose AnchorGT, a novel attention architecture for GTs with global receptive field and almost linear complexity, which serves as a flexible building block to improve the scalability of a wide range of GT models. Inspired by anchor-based GNNs, we employ structurally important $k$-dominating node set as anchors and design an attention mechanism that focuses on the relationship between individual nodes and anchors, while retaining the global receptive field for all nodes. With its intuitive design, AnchorGT can easily replace the attention module in various GT models with different network architectures and structural encodings, resulting in reduced computational overhead without sacrificing performance. In addition, we theoretically prove that AnchorGT attention can be strictly more expressive than Weisfeiler-Lehman test, showing its superiority in representing graph structures. Our experiments on three state-of-the-art GT models demonstrate that their AnchorGT variants can achieve better results while being faster and significantly more memory efficient.

• The paper introduces AnchorGT, which reduces computational complexity from quadratic to almost linear by using k-dominating nodes as anchors.
• It maintains a global receptive field, ensuring thorough graph structure analysis while integrating seamlessly with existing models.
• Empirical tests reveal that models with AnchorGT outperform or match state-of-the-art methods with significant improvements in training speed and memory efficiency.

AnchorGT: Enhancing Graph Transformers with Efficient and Scalable Attention Architecture

Introduction to Graph Transformers and Existing Challenges

Graph Transformers have extended the powerful self-attention mechanism of Transformers to the complex domain of graph data, opening up new possibilities in graph representation learning. However, a persistent challenge in deploying these architectures has been their scalability, largely due to the quadratic complexity involved in their self-attention mechanisms, especially as the number of graph nodes increases.

Existing solutions typically compromise either the global receptive field or the expressiveness of the model, which can detrimentally affect performance. This limitation poses a significant challenge when dealing with large-scale graphs commonly found in real-world scenarios like social networks or protein-interaction networks.

Overview of AnchorGT

The proposed AnchorGT architecture offers a novel solution to these scalability issues. AnchorGT introduces an attention architecture that operates with almost linear complexity while maintaining a global receptive field across all nodes. This is achieved through an inventive use of structurally significant nodes, termed as $k$-dominating nodes, which serve as anchors.

These anchors help in propagating information across the graph efficiently, reducing computational complexity significantly without sacrificing expressivity. The AnchorGT framework is versatile and can be incorporated into various existing graph Transformer models, seamlessly replacing their standard attention mechanisms.

Key Contributions and Theoretical Advancements

• Scalable Attention Mechanism: By integrating $k$-dominating set anchors into the attention mechanism, AnchorGT drastically reduces the computational overhead from quadratic to almost linear complexity.
• Retention of Global Receptive Field: Despite its efficiency, AnchorGT retains the global receptive field, a critical feature for capturing comprehensive graph structures.
• Enhanced Expressiveness: AnchorGT is theoretically proven to be more expressive than the Weisfeiler-Lehman graph isomorphism test. This implies that AnchorGT can distinguish between graph structures more effectively than some existing graph neural network models.

Empirical Validation

AnchorGT was tested against state-of-the-art graph Transformer models on standard benchmarks. The results were promising as models equipped with AnchorGT not only demonstrated better or comparable performance but also showcased significantly better efficiency in terms of memory usage and computational speed. Specifically, models with AnchorGT showed substantial reductions in training time and GPU memory consumption, affirming the practical benefits of the proposed architecture in handling large-scale graphs.

Looking Forward: Implications and Speculations

The flexibility and scalability of AnchorGT make it a potent tool for advancing graph Transformer models. Its ability to be integrated into various models could pave the way for new kinds of graph-based machine learning applications, potentially impacting areas such as bioinformatics, social network analysis, and beyond.

Moreover, the theoretical and empirical strengths of AnchorGT suggest that it could also influence future research direction in graph representation learning, possibly shifting focus towards more scalable and efficient architectures that do not compromise on performance.

Conclusion

AnchorGT presents a significant step forward in making graph Transformers more practical for large-scale applications. It offers a flexible, scalable, and expressively robust architecture that can effectively handle the complexities of large graph datasets while maintaining high performance. As such, it holds promise not only as a research tool but also as a component in applied machine learning systems dealing with complex network data.