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.
