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_{ℓ} = M_{ℓ} (x), (m_{ℓ})_{i} = \sum_{j \in N (i)} M_{ℓ} ((x_{ℓ})_{i}, (x_{ℓ})_{j}, A_{i j})

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_{ℓ})_{i} = U_{ℓ} ((x_{ℓ})_{i}, (m_{ℓ})_{i})

Mentions

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MPNNs can be expressed as graph convolutions
2025-02-17 graphs lecture 8
2025-02-25 equivariant lecture 4