Authors
Muhammet Balcilar, Pierre Héroux, Benoit Gauzere, Pascal Vasseur, Sébastien Adam, Paul Honeine
Publication date
2021/7/1
Conference
International Conference on Machine Learning
Pages
599-608
Publisher
PMLR
Description
Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their theoretical expressive power is limited to the first order Weisfeiler-Lehman test (1-WL). In this paper, we show that if the graph convolution supports are designed in spectral-domain by a non-linear custom function of eigenvalues and masked with an arbitrary large receptive field, the MPNN is theoretically more powerful than the 1-WL test and experimentally as powerful as a 3-WL existing models, while remaining spatially localized. Moreover, by designing custom filter functions, outputs can have various frequency components that allow the convolution process to learn different relationships between a given input graph signal and its associated properties. So far, the best 3-WL equivalent graph neural networks have a computational complexity in with memory usage in , consider non-local update mechanism and do not provide the spectral richness of output profile. The proposed method overcomes all these aforementioned problems and reaches state-of-the-art results in many downstream tasks.
Scholar articles
M Balcilar, P Héroux, B Gauzere, P Vasseur, S Adam… - International Conference on Machine Learning, 2021