Using a poset or directed graph as input for a neural network.

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As the title states, I'm trying to train a neural network using some unconventional input. I'm wondering if anyone has any experience or has read any papers that involve using a partially ordered set or alternatively a directed graph as an input for a neural network? Is there a way something like a directed graph can be effectively embedded as a vector? If so, I would greatly appreciate some guidance. Thanks

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A bit late, but have you looked at Graph Neural Networks? The representation of each node is updated from its neighbours representations. The neighbours could be the parent of a node only for example. There is a lot to it, so it's hard to summarize. The library PyTorchGeometric is well written with good documentation.

After N layers of GNN you can aggregate all the nodes together to get a fixed size vector representation. Alternatively you can add a "god" node that connects to everything and then use the representation of that node subsequently.

Not sure if it answers your question, but I stumbled here when looking more into these specific topics.