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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2406.03148 |
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| _version_ | 1866916274982879232 |
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| author | Müller, Luis Morris, Christopher |
| author_facet | Müller, Luis Morris, Christopher |
| contents | Graph neural network architectures aligned with the $k$-dimensional Weisfeiler--Leman ($k$-WL) hierarchy offer theoretically well-understood expressive power. However, these architectures often fail to deliver state-of-the-art predictive performance on real-world graphs, limiting their practical utility. While recent works aligning graph transformer architectures with the $k$-WL hierarchy have shown promising empirical results, employing transformers for higher orders of $k$ remains challenging due to a prohibitive runtime and memory complexity of self-attention as well as impractical architectural assumptions, such as an infeasible number of attention heads. Here, we advance the alignment of transformers with the $k$-WL hierarchy, showing stronger expressivity results for each $k$, making them more feasible in practice. In addition, we develop a theoretical framework that allows the study of established positional encodings such as Laplacian PEs and SPE. We evaluate our transformers on the large-scale PCQM4Mv2 dataset, showing competitive predictive performance with the state-of-the-art and demonstrating strong downstream performance when fine-tuning them on small-scale molecular datasets. Our code is available at https://github.com/luis-mueller/wl-transformers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aligning Transformers with Weisfeiler-Leman Müller, Luis Morris, Christopher Machine Learning Graph neural network architectures aligned with the $k$-dimensional Weisfeiler--Leman ($k$-WL) hierarchy offer theoretically well-understood expressive power. However, these architectures often fail to deliver state-of-the-art predictive performance on real-world graphs, limiting their practical utility. While recent works aligning graph transformer architectures with the $k$-WL hierarchy have shown promising empirical results, employing transformers for higher orders of $k$ remains challenging due to a prohibitive runtime and memory complexity of self-attention as well as impractical architectural assumptions, such as an infeasible number of attention heads. Here, we advance the alignment of transformers with the $k$-WL hierarchy, showing stronger expressivity results for each $k$, making them more feasible in practice. In addition, we develop a theoretical framework that allows the study of established positional encodings such as Laplacian PEs and SPE. We evaluate our transformers on the large-scale PCQM4Mv2 dataset, showing competitive predictive performance with the state-of-the-art and demonstrating strong downstream performance when fine-tuning them on small-scale molecular datasets. Our code is available at https://github.com/luis-mueller/wl-transformers. |
| title | Aligning Transformers with Weisfeiler-Leman |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2406.03148 |