NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs (2206.04910v4)

Abstract: The graph Transformer emerges as a new architecture and has shown superior performance on various graph mining tasks. In this work, we observe that existing graph Transformers treat nodes as independent tokens and construct a single long sequence composed of all node tokens so as to train the Transformer model, causing it hard to scale to large graphs due to the quadratic complexity on the number of nodes for the self-attention computation. To this end, we propose a Neighborhood Aggregation Graph Transformer (NAGphormer) that treats each node as a sequence containing a series of tokens constructed by our proposed Hop2Token module. For each node, Hop2Token aggregates the neighborhood features from different hops into different representations and thereby produces a sequence of token vectors as one input. In this way, NAGphormer could be trained in a mini-batch manner and thus could scale to large graphs. Moreover, we mathematically show that as compared to a category of advanced Graph Neural Networks (GNNs), the decoupled Graph Convolutional Network, NAGphormer could learn more informative node representations from the multi-hop neighborhoods. Extensive experiments on benchmark datasets from small to large are conducted to demonstrate that NAGphormer consistently outperforms existing graph Transformers and mainstream GNNs. Code is available at https://github.com/JHL-HUST/NAGphormer.

An Analytical Perspective on NAGphormer: A Tokenized Graph Transformer for Scalable Node Classification

The paper under discussion introduces NAGphormer, an innovative graph Transformer architecture designed to efficiently perform node classification tasks on large-scale graphs. The novelty in NAGphormer lies in its foundational idea of viewing each node as a sequence formed by tokenizing its neighborhood features through a proposed Hop2Token module, thereby enabling scalability and enhanced information capture.

Core Innovations and Architectural Design

Traditional graph Transformers face scalability issues due to their inherent quadratic complexity related to node count in their self-attention computations. The NAGphormer model proposes to address this challenge through its Hop2Token module, which transforms neighborhood features into token sequences. Each node in the graph, thus, consists of a series of token vectors created by aggregating features from multiple hops. This tokenization process allows the model to train using mini-batch methods, affording scalability from small to large graph datasets.

Hop2Token is pivotal in aggregating different hop neighborhood features into distinct representations, turning them into token sequences for input into the Transformer. This approach enables NAGphormer to preserve multi-hop neighborhood information effectively, addressing the limitations of conventional Graph Neural Networks (GNNs), such as over-smoothing and the message-passing bottleneck.

Comparative and Computational Analysis

Theoretical analysis reveals that NAGphormer can assimilate richer node representations from multi-hop neighborhoods when compared with decoupled GCNs, due to its dynamic attention-based mechanism. This ability is facilitated by the attention-based readout function, which adaptively weighs the contributions of different-hop neighborhoods, a feature that is absent in traditional message-passing-based GNNs.

Experimentally, NAGphormer is validated against multiple baselines, including both GNNs and existing graph Transformers, across nine benchmark datasets. It consistently demonstrates superior performance, notably in handling large-scale graphs where traditional graph Transformers struggle due to computational constraints. The results are robust across datasets ranging from academia-focused networks, such as Pubmed and CoraFull, to large-scale network data like Amazon2M and Reddit.

Implications for Future Research

The success of NAGphormer underscores the feasibility of applying Transformer-based architectures to non-Euclidean data like graphs. This architecture's ability to scale efficiently with graph size while maintaining or surpassing the performance of existing models suggests potential broad applications in domains requiring analysis of large, complex networks, such as social network analysis, bioinformatics, and recommendation systems.

The paper proposes an intriguing direction for future work in extending the NAGphormer framework to other graph-based tasks, potentially incorporating edge features or handling dynamic graphs. Moreover, its approach of treating graph nodes analogously to natural language sequences could inspire cross-domain applications or adaptations beyond traditional graph mining tasks.

Conclusion

NAGphormer is a noteworthy contribution to the space of graph Transformers, successfully balancing the complexity and scalability challenges of node classification in large graphs through its token-based sequence approach. By circumventing the common pitfalls associated with message-passing mechanisms in GNNs and leveraging the attention mechanism of Transformers, it presents a powerful framework potentially extensible to broader applications and research in graph-based deep learning.