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Gradformer: Graph Transformer with Exponential Decay (2404.15729v1)

Published 24 Apr 2024 in cs.LG

Abstract: Graph Transformers (GTs) have demonstrated their advantages across a wide range of tasks. However, the self-attention mechanism in GTs overlooks the graph's inductive biases, particularly biases related to structure, which are crucial for the graph tasks. Although some methods utilize positional encoding and attention bias to model inductive biases, their effectiveness is still suboptimal analytically. Therefore, this paper presents Gradformer, a method innovatively integrating GT with the intrinsic inductive bias by applying an exponential decay mask to the attention matrix. Specifically, the values in the decay mask matrix diminish exponentially, correlating with the decreasing node proximities within the graph structure. This design enables Gradformer to retain its ability to capture information from distant nodes while focusing on the graph's local details. Furthermore, Gradformer introduces a learnable constraint into the decay mask, allowing different attention heads to learn distinct decay masks. Such an design diversifies the attention heads, enabling a more effective assimilation of diverse structural information within the graph. Extensive experiments on various benchmarks demonstrate that Gradformer consistently outperforms the Graph Neural Network and GT baseline models in various graph classification and regression tasks. Additionally, Gradformer has proven to be an effective method for training deep GT models, maintaining or even enhancing accuracy compared to shallow models as the network deepens, in contrast to the significant accuracy drop observed in other GT models.Codes are available at \url{https://github.com/LiuChuang0059/Gradformer}.

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Authors (6)
  1. Chuang Liu (71 papers)
  2. Zelin Yao (4 papers)
  3. Yibing Zhan (73 papers)
  4. Xueqi Ma (13 papers)
  5. Shirui Pan (198 papers)
  6. Wenbin Hu (50 papers)
Citations (1)
View on Semantic Scholar

Summary

Integrating Inductive Bias into Graph Transformers with Gradformer

Overview of Gradformer

Gradformer presents a novel approach by integrating an exponential decay mask into the Graph Transformer (GT) self-attention mechanism. This integration explicitly accounts for the structural inductive biases inherently present in graph data, which have been inadequately addressed by previous GT models.

Key Contributions and Findings

  • Exponential Decay Mask: Gradformer applies an exponential decay mask to the attention scores within the GT framework. This mask ensures that attention weights diminish exponentially with increasing node distance, which helps prioritize local structural information and diminish the influence of distant nodes.
  • Learnable Structural Focusing: The introduced decay mask is not static but includes a learnable parameter that allows the model to adaptively focus on varying graph structural nuances. This adaptation is crucial for the model to dynamically emphasize different localities in the graph depending on the task at hand.
  • Empirical Validation: Extensive testing on various graph benchmarks demonstrates that Gradformer consistently outperforms both traditional Graph Neural Network models and other state-of-the-art GT models across multiple graph classification and regression tasks.

Detailed Methodology Analysis

Architecture

Gradformer modifies the traditional GT architecture by incorporating a decay mask derived from the graph's structural properties. The attention mask, defined by an exponential function relative to the node distances, is employed during the attention mechanism computation, enhancing the model's focus on structurally significant elements while filtering out distant and potentially irrelevant nodes.

Computational Implications

The primary computational overhead introduced by Gradformer arises from the calculation of the decay mask and its application to the attention mechanism. Despite this additional step, the overall computational complexity remains efficient, making Gradformer a feasible solution for large-scale applications.

Experimental Insights

Benchmark Performance

On established graph dataset benchmarks such as those from the OGB and TU collections, Gradformer sets new performance standards. Particularly in deeper network configurations, where previous GT models tend to lose accuracy, Gradformer maintains or even improves performance, indicating robustness and better utilization of deep network capabilities in graph structured tasks.

Efficiency and Scalability

The introduced method shows enhanced efficiency and scalability, managing higher accuracy without a substantial increase in computational demand. This balance is crucial for the practical application of GTs in resource-intensive scenarios.

Future Directions

Looking forward, there are several avenues for advancing Gradformer's initial promising results:

  1. Extended Structural Bias Integration: Further research could explore more sophisticated forms of structural biases that could be integrated into the decay mask, potentially improving the model’s ability to capture complex graph topologies.
  2. Adaptation to Various Graph Tasks: While the current implementation focuses on graph classification and regression, future modifications could adapt Gradformer for other graph-related tasks, such as link prediction or community detection.
  3. Theoretical Analysis: A deeper theoretical understanding of how the exponential decay mask influences learning in GTs would provide insights into optimizing model architecture and training processes for specific kinds of graph data.

In summary, Gradformer introduces an innovative methodology to enhance Graph Transformers by robustly incorporating graph structural biases, demonstrating significant improvements over existing methods. The versatility and scalability of Gradformer suggest a wide range of potential applications and substantial contributions to the field of graph machine learning.

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