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graph_neural_networks (1321B)


      1 # Graph neural networks (GNN)
      2 
      3 A kind of [distributed_algorithm] on a [graph], related to [message_passing], to compute a [function]
      4 
      5 - initially every node of the graph is mapped to a vector of [real_numbers]
      6 - at every step, you [aggregate] coordinatewise the state of the [neighbors], and then you use a [combination_function] with the previous node state and the aggregate states of the neighbors
      7   - the [aggregation] function can be [sum], [mean], or [max] (coordinatewise)
      8   - the [combination_function] is computed by a [feedforward_neural_network] (multilayer [perceptron])
      9 
     10 Extensions:
     11 - [global_aggregation]: add a value which is obtained by aggregating the state of all nodes, and is passed to the [combination_function]
     12 - [random_initialization]: include in the initial label of the nodes one [random] number
     13 
     14 The network computes a value on every node. We can also use a [readout_function] to get a final value out of the entire graph: computed by a [feedforward_neural_network] from the result of applying an [aggregation_function] to the state of all nodes
     15 
     16 Observation:
     17 - On [graph_isomorphic] [graphs], the value of the function computed by a GNN is the same
     18 
     19 - [graph_neural_network_expressiveness]
     20 
     21 Other model: [GNN_recurrent]
     22 
     23 Up: [graph], [neural_network]
     24 
     25 Aliases: graph neural network, GNN, GNNs