TRIPODS Winter School & Workshop-Gitta Kutyniok
Title- Transferability: Spectral Graph Convolutional Neural Networks Do Generalize
Abstract– The success of convolutional neural networks on Euclidean domains ignited an interest in recent years in extending these methods to graph structured data. This led to spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. Since often the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signals on graphs unseen in the training set. The term “transferability” then refers to the condition that a single filter or ConvNet has similar repercussions on both graphs, if two graphs describe the same phenomenon. However, for a long time it was believed that spectral filters are not transferable. In this talk we aim to debunking this common misconception by showing that if two graphs discretize the same continuous metric space, then a spectral filter or ConvNet has approximately the same repercussion on both graphs. Our analysis even accounts for large graph perturbations as well as allows graphs to have completely different dimensions and topologies, only requiring that both graphs discretize the same underlying continuous space. (Joint work with R. Levie, W. Huang, L. Bucci, and M. Bronstein.)