Title :
Computational Capabilities of Graph Neural Networks
Author :
Scarselli, Franco ; Gori, Marco ; Tsoi, Ah Chung ; Hagenbuchner, Markus ; Monfardini, Gabriele
Author_Institution :
Fac. of Inf. Eng., Univ. of Siena, Siena
Abstract :
In this paper, we will consider the approximation properties of a recently introduced neural network model called graph neural network (GNN), which can be used to process-structured data inputs, e.g., acyclic graphs, cyclic graphs, and directed or undirected graphs. This class of neural networks implements a function tau(G, n) isin R m that maps a graph G and one of its nodes n onto an m-dimensional Euclidean space. We characterize the functions that can be approximated by GNNs, in probability, up to any prescribed degree of precision. This set contains the maps that satisfy a property called preservation of the unfolding equivalence, and includes most of the practically useful functions on graphs; the only known exception is when the input graph contains particular patterns of symmetries when unfolding equivalence may not be preserved. The result can be considered an extension of the universal approximation property established for the classic feedforward neural networks (FNNs). Some experimental examples are used to show the computational capabilities of the proposed model.
Keywords :
approximation theory; graph theory; neural nets; Euclidean space; acyclic graphs; computational capabilities; cyclic graphs; directed graphs; feedforward neural networks; graph neural networks; neural network model; structured data inputs; undirected graphs; Approximation theory; graph neural networks (GNNs); graphical domains; universal approximators; Algorithms; Neural Networks (Computer); Pattern Recognition, Automated;
Journal_Title :
Neural Networks, IEEE Transactions on
Conference_Location :
12/9/2008 12:00:00 AM
DOI :
10.1109/TNN.2008.2005141