Breaking the Limits of Message Passing Graph Neural Networks

Muhammet Balcilar (1, 2) , Pierre Héroux (1) , Benoit Gaüzère (1) , Pascal Vasseur (3, 1) , Sébastien Adam (1) , Paul Honeine (1)

1 DocApp - LITIS - Equipe Apprentissage
2 InterDigital R&D France
3 MIS - Modélisation, Information et Systèmes - UR UPJV 4290

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 nonlinear 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 O(n^3) with memory usage in O(n^2), 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.

Domaines: Machine Learning [stat.ML]; Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]; Réseau de neurones [cs.NE]; Apprentissage [cs.LG]; Ordinateur et société [cs.CY]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Muhammet Balcilar, Pierre Héroux, Benoit Gaüzère, Pascal Vasseur, Sébastien Adam, et al.. Breaking the Limits of Message Passing Graph Neural Networks. Proceedings of the 38th International Conference on Machine Learning (ICML), Jul 2021, Vienna, Austria. pp.599-608. ⟨hal-03410699⟩