Spectral Networks and Locally Connected Networks on Graphs

The paper investigates how to extend convolutional neural networks, which are efficient on images and audio because they exploit local translational invariance, to signals defined on more general domains that lack the action of a translation group. It proposes two ways to construct convolution-like layers on such domains: one based on a hierarchical clustering of the domain (a spatial construction), and another based on the spectrum of the graph Laplacian (a spectral construction).

Through experiments, the authors show that for low-dimensional graphs it is possible to learn convolutional layers whose number of parameters is independent of the input size, resulting in efficient deep architectures. This work was an early foundation for graph neural networks, demonstrating that the parameter-sharing efficiency of CNNs could be carried over to graph-structured, non-Euclidean data.