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PDE-CNNs: Axiomatic Derivations and Applications
PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) utilize solvers of geometrically meaningful evolution PDEs as substitutes for the conventional components in G-CNNs.
Optimal Transport on the Lie Group of Roto-translations
We develop a Sinkhorn like algorithm that can be efficiently implemented using fast and accurate distance approximations of the Lie group and GPU-friendly group convolutions.
Analysis of (sub-)Riemannian PDE-G-CNNs
Typically, G-CNNs have the advantage over CNNs that they do not waste network capacity on training symmetries that should have been hard-coded in the network.
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