ChebLieNet: A Graph Neural Network with anisotropic Anisotropies

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Source arXiv

Machine Learning

Stats Machine Learning

ChebLieNet: A Graph Neural Network with anisotropic Anisotropies

ChebLieNet: Invariant Spectral Graph NNs Turned Equivariant by Riemannian Geometry on Lie Groups

We introduce a new approach to exploit any anisotropies in data.

Surfing on the success of graph-and group-based neural networks, we take advantage of the recent developments in the geometric deep learning field to derive a new approach to exploit any anisotropies in data.

Via discrete approximations of lie groups, we develop a graph neural network made of anisotropic convolutional layers (chebyshev convolutions), spatial pooling and unpooling layers, and global pooling layers.

Group equivariance is achieved via equivariant and invariant operators on graphs with anisotropic left-invariantriemannian distance-based affinities encoded on the edges.

This control on anisotropies of the metrics allows to balance equivariance (anisotropic metric) against invariance (isotropic metric) of the graph convolution layers.

We also evaluate the scalability of this approach on stl10 (image data) and climatenet (spherical data), showing its remarkable adaptability to diverse tasks.

Authors

Hugo Aguettaz, Erik J. Bekkers, Michaël Defferrard

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