Orbit-equivariant graph neural networks
Equivariance is an important structural property that is captured by architectures such as graph neural networks (GNNs). However, equivariant graph functions cannot produce different outputs for similar nodes, which may be undesirable when the function is trying to optimize some global graph propert...
| Main Authors: | , , |
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| Format: | Conference item |
| Language: | English |
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OpenReview
2024
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| _version_ | 1811140718338506752 |
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| author | Morris, M Grau, BC Horrocks, I |
| author_facet | Morris, M Grau, BC Horrocks, I |
| author_sort | Morris, M |
| collection | OXFORD |
| description | Equivariance is an important structural property that is captured by architectures such as graph neural networks (GNNs). However, equivariant graph functions cannot produce different outputs for similar nodes, which may be undesirable when the function is trying to optimize some global graph property. In this paper, we define orbit-equivariance, a relaxation of equivariance which allows for such functions whilst retaining important structural inductive biases. We situate the property in the hierarchy of graph functions, define a taxonomy of orbit-equivariant functions, and provide four different ways to achieve non-equivariant GNNs. For each, we analyze their expressivity with respect to orbit-equivariance and evaluate them on two novel datasets, one of which stems from a real-world use-case of designing optimal bioisosteres. |
| first_indexed | 2024-09-25T04:26:26Z |
| format | Conference item |
| id | oxford-uuid:e15aafc8-63e0-4cb9-9176-943b187e1d47 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:26:26Z |
| publishDate | 2024 |
| publisher | OpenReview |
| record_format | dspace |
| spelling | oxford-uuid:e15aafc8-63e0-4cb9-9176-943b187e1d472024-08-23T16:30:47ZOrbit-equivariant graph neural networksConference itemhttp://purl.org/coar/resource_type/c_5794uuid:e15aafc8-63e0-4cb9-9176-943b187e1d47EnglishSymplectic ElementsOpenReview2024Morris, MGrau, BCHorrocks, IEquivariance is an important structural property that is captured by architectures such as graph neural networks (GNNs). However, equivariant graph functions cannot produce different outputs for similar nodes, which may be undesirable when the function is trying to optimize some global graph property. In this paper, we define orbit-equivariance, a relaxation of equivariance which allows for such functions whilst retaining important structural inductive biases. We situate the property in the hierarchy of graph functions, define a taxonomy of orbit-equivariant functions, and provide four different ways to achieve non-equivariant GNNs. For each, we analyze their expressivity with respect to orbit-equivariance and evaluate them on two novel datasets, one of which stems from a real-world use-case of designing optimal bioisosteres. |
| spellingShingle | Morris, M Grau, BC Horrocks, I Orbit-equivariant graph neural networks |
| title | Orbit-equivariant graph neural networks |
| title_full | Orbit-equivariant graph neural networks |
| title_fullStr | Orbit-equivariant graph neural networks |
| title_full_unstemmed | Orbit-equivariant graph neural networks |
| title_short | Orbit-equivariant graph neural networks |
| title_sort | orbit equivariant graph neural networks |
| work_keys_str_mv | AT morrism orbitequivariantgraphneuralnetworks AT graubc orbitequivariantgraphneuralnetworks AT horrocksi orbitequivariantgraphneuralnetworks |