Graph neural network

A graph neural network (GNN) is a class of artificial neural networks for processing data that can be represented as graphs. In the more general subject of "geometric deep learning", certain existing neural network architectures can be interpreted as GNNs operating on suitably defined graphs. Convolutional neural networks, in the context of computer vision, can be seen as a GNN applied to graphs structured as grids of pixels. Transformers, in the context of natural language processing, can be seen as GNNs applied to complete graphs whose nodes are words in a sentence. The key design element of GNNs is the use of pairwise message passing, such that graph nodes iteratively update their representations by exchanging information with their neighbors. Since their inception, several different GNN architectures have been proposed, which implement different flavors of message passing, started by recursive or convolutional constructive approaches. , whether it is possible to define GNN architectures "going beyond" message passing, or if every GNN can be built on message passing over suitably defined graphs, is an open research question. Relevant application domains for GNNs include Natural Language Processing, social networks, citation networks, molecular biology, chemistry, physics and NP-hard combinatorial optimization problems. Several open source libraries implementing graph neural networks are available, such as PyTorch Geometric (PyTorch), TensorFlow GNN (TensorFlow), and jraph (Google JAX). The architecture of a generic GNN implements the following fundamental layers: Permutation equivariant: a permutation equivariant layer maps a representation of a graph into an updated representation of the same graph. In the literature, permutation equivariant layers are implemented via pairwise message passing between graph nodes. Intuitively, in a message passing layer, nodes update their representations by aggregating the messages received from their immediate neighbours. As such, each message passing layer increases the receptive field of the GNN by one hop.