Geometric Adaptations of PDE-G-CNNs

Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. The recently introduced framework of PDE-based G-CNNs (PDE-G-CNNs) generalizes G-CNNs while simultaneously reducing network complexity and increasing performance. In PDE-G-CNNs the usual building blocks of neural networks are replaced with solvers for evolution PDEs, these PDEs being convection, diffusion, dilation, and erosion. We investigate three geometric adaptations of PDE-G-CNNs: