Neural networks applied to graph data.
(Neural networks of course can already be *represented* as directed graphs, or applied to phenomena which arise from a causal graph but that is not what we mean here.

The version of graphical neural nets with which I am familiar is applying convnets to spectral graph representations. e.g. Thomas Kipf summarises research there.

I gather that the field has moved on and I am no longer across what is happening.

See perhaps Xavier Besson’s implementation of one graph convnet. Maybe check out Chaitanya Joshi’s overviews of spatial graph convnets and his attempt to link them to attention mechanisms.

Facebook’s GTN might be a tool here:

GTN is an open source framework for automatic differentiation with a powerful, expressive type of graph called weighted finite-state transducers (WFSTs). Just as PyTorch provides a framework for automatic differentiation with tensors, GTN provides such a framework for WFSTs. AI researchers and engineers can use GTN to more effectively train graph-based machine learning models.

I have not used GTN so I cannot say if I have field it correctly or if it is more of a computational graph learning tool.

Distance Encoding is a general class of graph-structure-related features that can be utilized by graph neural networks to improve the structural representation power. Given a node set whose structural representation is to be learnt, DE for a node over the graph is defined as a mapping of a set of landing probabilities of random walks from each node of the node set of interest to this node. Distance encoding generally includes measures such as shortest-path-distances and generalized PageRank scores. Distance encoding can be merged into the design of graph neural networks in simple but effective ways: First, we propose DEGNN that utilizes distance encoding as extra node features. We further enhance DEGNN by allowing distance encoding to control the aggregation procedure of traditional GNNs, which yields another model DEAGNN. Since distance encoding purely depends on the graph structure and is independent from node identifiers, it has inductive and generalization ability.

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