Transformers Meet Directed Graphs

Simon Geisler, Yujia Li, Daniel J Mankowitz, Ali Taylan Cemgil, Stephan Günnemann, Cosmin Paduraru
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:11144-11172, 2023.

Abstract

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%.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-geisler23a, title = {Transformers Meet Directed Graphs}, author = {Geisler, Simon and Li, Yujia and Mankowitz, Daniel J and Cemgil, Ali Taylan and G\"{u}nnemann, Stephan and Paduraru, Cosmin}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {11144--11172}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/geisler23a/geisler23a.pdf}, url = {https://proceedings.mlr.press/v202/geisler23a.html}, abstract = {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%.} }
Endnote
%0 Conference Paper %T Transformers Meet Directed Graphs %A Simon Geisler %A Yujia Li %A Daniel J Mankowitz %A Ali Taylan Cemgil %A Stephan Günnemann %A Cosmin Paduraru %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-geisler23a %I PMLR %P 11144--11172 %U https://proceedings.mlr.press/v202/geisler23a.html %V 202 %X 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%.
APA
Geisler, S., Li, Y., Mankowitz, D.J., Cemgil, A.T., Günnemann, S. & Paduraru, C.. (2023). Transformers Meet Directed Graphs. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:11144-11172 Available from https://proceedings.mlr.press/v202/geisler23a.html.

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