Breaking the Limits of Message Passing Graph Neural Networks

Muhammet Balcilar, Pierre Heroux, Benoit Gauzere, Pascal Vasseur, Sebastien Adam, Paul Honeine
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:599-608, 2021.

Abstract

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 $\mathcal{O}(n^3)$ with memory usage in $\mathcal{O}(n^2)$, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-balcilar21a, title = {Breaking the Limits of Message Passing Graph Neural Networks}, author = {Balcilar, Muhammet and Heroux, Pierre and Gauzere, Benoit and Vasseur, Pascal and Adam, Sebastien and Honeine, Paul}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {599--608}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/balcilar21a/balcilar21a.pdf}, url = {https://proceedings.mlr.press/v139/balcilar21a.html}, abstract = {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 $\mathcal{O}(n^3)$ with memory usage in $\mathcal{O}(n^2)$, 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.} }
Endnote
%0 Conference Paper %T Breaking the Limits of Message Passing Graph Neural Networks %A Muhammet Balcilar %A Pierre Heroux %A Benoit Gauzere %A Pascal Vasseur %A Sebastien Adam %A Paul Honeine %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-balcilar21a %I PMLR %P 599--608 %U https://proceedings.mlr.press/v139/balcilar21a.html %V 139 %X 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 $\mathcal{O}(n^3)$ with memory usage in $\mathcal{O}(n^2)$, 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.
APA
Balcilar, M., Heroux, P., Gauzere, B., Vasseur, P., Adam, S. & Honeine, P.. (2021). Breaking the Limits of Message Passing Graph Neural Networks. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:599-608 Available from https://proceedings.mlr.press/v139/balcilar21a.html.

Related Material