Neural networks applied to graph data. (Neural networks of course can already be represented as directed graphs, or applied to phenomena which arised from a causal graph but that is not an immediate concern.
The version of graphical neural nets with which I am familar 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 reallya cross what is happening there.
Xavier Besson’s implementation of one graph convnet.
See Chaitanya Joshi’s overviews of spatial graph convnets and his attempt to link them to attention mechanisms.
Bresson, Xavier, and Thomas Laurent. 2018. “An Experimental Study of Neural Networks for Variable Graphs,” 4.
Bronstein, Michael M., Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. 2017. “Geometric Deep Learning: Going Beyond Euclidean Data.” IEEE Signal Processing Magazine 34 (4): 18–42. https://doi.org/10.1109/MSP.2017.2693418.
Bui, Thang D., Sujith Ravi, and Vivek Ramavajjala. 2017. “Neural Graph Machines: Learning Neural Networks Using Graphs,” March. http://arxiv.org/abs/1703.04818.
Cranmer, Miles D, Rui Xu, Peter Battaglia, and Shirley Ho. 2019. “Learning Symbolic Physics with Graph Networks.” In Machine Learning and the Physical Sciences Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS), 6.
Defferrard, Michaël, Xavier Bresson, and Pierre Vandergheynst. 2016. “Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering.” In Advances in Neural Information Processing Systems. http://arxiv.org/abs/1606.09375.
Dwivedi, Vijay Prakash, Chaitanya K. Joshi, Thomas Laurent, Yoshua Bengio, and Xavier Bresson. 2020. “Benchmarking Graph Neural Networks,” July. http://arxiv.org/abs/2003.00982.
Lamb, Luis C., Artur Garcez, Marco Gori, Marcelo Prates, Pedro Avelar, and Moshe Vardi. 2020. “Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective.” In IJCAI 2020. http://arxiv.org/abs/2003.00330.
Ng, Ignavier, Shengyu Zhu, Zhitang Chen, and Zhuangyan Fang. 2019. “A Graph Autoencoder Approach to Causal Structure Learning.” In Advances in Neural Information Processing Systems. http://arxiv.org/abs/1911.07420.
Sanchez-Gonzalez, Alvaro, Victor Bapst, Peter Battaglia, and Kyle Cranmer. 2019. “Hamiltonian Graph Networks with ODE Integrators.” In Machine Learning and the Physical Sciences Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS), 11.