{"url":"/method/mpnn","slug":"mpnn","name":"MPNN","full_name":"Message Passing Neural Network","full_name_withheld":false,"description_markdown":"There are at least eight notable examples of models from the literature that can be described using the **Message Passing Neural Networks** (**MPNN**) framework. For simplicity we describe MPNNs which operate on undirected graphs $G$ with node features $x_{v}$ and edge features $e_{vw}$. It is trivial to extend the formalism to directed multigraphs. The forward pass has two phases, a message passing phase and a readout phase. The message passing phase runs for $T$ time steps and is defined in terms of message functions $M_{t}$ and vertex update functions $U_{t}$. During the message passing phase, hidden states $h_{v}^{t}$ at each node in the graph are updated based on messages $m_{v}^{t+1}$ according to\r\n$$\r\nm_{v}^{t+1} = \\sum_{w \\in N(v)} M_{t}(h_{v}^{t}, h_{w}^{t}, e_{vw})\r\n$$\r\n$$\r\nh_{v}^{t+1} = U_{t}(h_{v}^{t}, m_{v}^{t+1})\r\n$$\r\nwhere in the sum, $N(v)$ denotes the neighbors of $v$ in graph $G$. The readout phase computes a feature vector for the whole graph using some readout function $R$ according to\r\n$$\r\n\\hat{y} = R(\\\\{ h_{v}^{T} | v \\in G \\\\})\r\n$$\r\nThe message functions $M_{t}$, vertex update functions $U_{t}$, and readout function $R$ are all learned differentiable functions. $R$ operates on the set of node states and must be invariant to permutations of the node states in order for the MPNN to be invariant to graph isomorphism.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Neural Message Passing for Quantum Chemistry","paper":"/paper/neural-message-passing-for-quantum-chemistry","first_author":"Justin Gilmer","n_authors":5,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/neural-message-passing-for-quantum-chemistry"},"source":{"url":"http://arxiv.org/abs/1704.01212v2","title":"Neural Message Passing for Quantum 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