Simon Geisler, Yujia Li, Daniel Mankowitz, Ali Taylan Cemgil, Stephan Günnemann, Cosmin Paduraru
Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains, including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Graph Property Prediction | ogbg-code2 | Number of params | 14378069 | SAT++ with Magnetic Laplacian |
| Graph Property Prediction | ogbg-code2 | Number of params | 14378069 | SAT++ with Magnetic Laplacian |