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In graph neural networks, the Banach fixed-point theorem and Jacobi method it is described that the transition from one state to another be defined by a contraction map with a fixed-point.

The autor states:

"The transition function in a GNN is assumed to be a contractive mapping with respect to the nodes’ state".

But in practice these output and transition functions are modeled using feed-forward networks, specifically an RNN. Which to my knowledge can represent any function and is not constrained to be a contraction map.

My learning is from this article https://towardsdatascience.com/graph-neural-networks-20d0f8da7df6, which describes what I said above but somewhat vaguely.

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  • $\begingroup$ In that article, the author says "The transition function in a GNN is assumed to be a contractive mapping with respect to the nodes’ state". They don't say that FFNNs are contraction mappings. Can you please edit your post to clarify this and your question? $\endgroup$ – nbro May 18 '20 at 21:40
  • $\begingroup$ Sure, no problem thank you for pointing this out! $\endgroup$ – Jacob B May 18 '20 at 21:44

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