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- W4310632097 abstract "We define the bicategory of Graph Convolutional Neural Networks $mathbf{GCNN}_n$ for an arbitrary graph with $n$ nodes. We show it can be factored through the already existing categorical constructions for deep learning called $mathbf{Para}$ and $mathbf{Lens}$ with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor $mathbf{GCNN}_n to mathbf{Para}(mathsf{CoKl}(mathbb{R}^{n times n} times -))$. We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions." @default.
- W4310632097 created "2022-12-13" @default.
- W4310632097 creator A5041889305 @default.
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- W4310632097 date "2022-12-01" @default.
- W4310632097 modified "2023-10-16" @default.
- W4310632097 title "Graph Convolutional Neural Networks as Parametric CoKleisli morphisms" @default.
- W4310632097 doi "https://doi.org/10.48550/arxiv.2212.00542" @default.
- W4310632097 hasPublicationYear "2022" @default.
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