message passing neural network

[[concept]]

Message Passing Neural Network (MPNN)

This type of network was initially introduced by Gilmer et al. In a message passing neural network, each layer consists of 2 operations: the message and the update.

The message is a function that processes

• the signal at node $i$
• the message /signal at each of the neighbors of $i$
• the edge weights $m_{\ell }=M_{\ell }(x),(m_{\ell }{)}_i={\sum }_{j\in N(i)}{M}_{\ell }((x_{\ell }{)}_i,(x_{\ell }{)}_j,A_{ij})$

The update is a function on the signal of the graph from the previous layer to the next, taking into account the message and the current value at each node: $(x_{\ell }{)}_i=U_{\ell }((x_{\ell }{)}_i,(m_{\ell }{)}_i)$

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