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As far I know, the RNN accepts a sequence as input and can produce as a sequence as output.

Are there neural networks that accept graphs or trees as inputs, so that to represent the relationships between the nodes of the graph or tree?

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There are types of neural networks designed exactly for that purpose. For example, graph convolutional networks (GCN) by Thomas N. Kipf. The input to the network will be a matrix of size $N \times F$, where $N$ is the number of nodes and $F$ the number of features (for each node). You then can multiply the feature matrix with the adjacency matrix (each node is going to be a weighted sum of its first-degree neighbors). There are a lot of other variations, such as diffusion convolutional networks, gated graph neural networks, etc. There is a nice survey that describes most of the recent related work in the field Graph Neural Networks: A review of methods and applications by Jie Zhou et al.

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    $\begingroup$ 'The input to the network will be a matrix of size NxF' of fixed size, i guess? $\endgroup$ – user8426627 Jun 6 at 12:10
  • $\begingroup$ Yes, usually the input if fixed. Is that a problem for your setting? $\endgroup$ – razvanc92 Jun 7 at 8:44

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