Enhancing Graph Transformers with Hierarchical Distance Structural Encoding
This addresses the need for better graph representation learning in domains like molecules and social networks, but it is incremental as it builds on existing graph transformer frameworks.
The paper tackled the problem of graph transformers lacking inductive biases for capturing hierarchical structures in graphs, and the result was a Hierarchical Distance Structural Encoding (HDSE) method that improved performance on graph classification, regression across 7 datasets, and node classification on 11 large-scale graphs, including those with up to a billion nodes.
Graph transformers need strong inductive biases to derive meaningful attention scores. Yet, current methods often fall short in capturing longer ranges, hierarchical structures, or community structures, which are common in various graphs such as molecules, social networks, and citation networks. This paper presents a Hierarchical Distance Structural Encoding (HDSE) method to model node distances in a graph, focusing on its multi-level, hierarchical nature. We introduce a novel framework to seamlessly integrate HDSE into the attention mechanism of existing graph transformers, allowing for simultaneous application with other positional encodings. To apply graph transformers with HDSE to large-scale graphs, we further propose a high-level HDSE that effectively biases the linear transformers towards graph hierarchies. We theoretically prove the superiority of HDSE over shortest path distances in terms of expressivity and generalization. Empirically, we demonstrate that graph transformers with HDSE excel in graph classification, regression on 7 graph-level datasets, and node classification on 11 large-scale graphs, including those with up to a billion nodes.