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All smooth manifolds can be realised as submanifolds of euclidean space. This is the famous Nash embedding theorem: https://en.wikipedia.org/wiki/Nash_embedding
by bollu 6y ago
All smooth manifolds can be realised as submanifolds of euclidean space. This is the famous Nash embedding theorem: https://en.wikipedia.org/wiki/Nash_embedding_theorem https://en.wikipedia.org/wiki/Nash_embedding_theorem
Hence, it's unclear if the power gained by GNNs is actually 'useful'.
- grandmczeb 6y agoWhat do you mean by useful? GNNs get better performance than other methods on lots of real tasks. It's the same as CNNs being useful in practice despite not having more "theoretical" power than MLPs.
- lostmsu 6y agoWhich tasks where GNNs get better performance have standardized benchmarks?