Bridging Graph Position Encodings for Transformers with Weighted Graph-Walking Automata
This work addresses the challenge of adapting transformers for graph data, which is important for applications in domains like social networks or biology, but it appears incremental as it builds on existing PE methods.
The authors tackled the problem of enabling transformers to operate on graph-structured data by introducing Graph Automaton PE (GAPE), a new positional encoding based on weighted graph-walking automata, and showed that it generalizes several other PEs and performs competitively in experiments on machine translation and graph tasks.
A current goal in the graph neural network literature is to enable transformers to operate on graph-structured data, given their success on language and vision tasks. Since the transformer's original sinusoidal positional encodings (PEs) are not applicable to graphs, recent work has focused on developing graph PEs, rooted in spectral graph theory or various spatial features of a graph. In this work, we introduce a new graph PE, Graph Automaton PE (GAPE), based on weighted graph-walking automata (a novel extension of graph-walking automata). We compare the performance of GAPE with other PE schemes on both machine translation and graph-structured tasks, and we show that it generalizes several other PEs. An additional contribution of this study is a theoretical and controlled experimental comparison of many recent PEs in graph transformers, independent of the use of edge features.