Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks

Explore the functional properties of PDE-based Group Equivariant Convolutional Neural Networks (PDE-G-CNNs) in this 21-minute conference talk from GSI. Delve into the recently introduced PDE-G-CNN framework, which proposes non-linear morphological convolutions motivated by solving HJB-PDEs on lifted homogeneous spaces. Discover how these networks generalize G-CNNs and achieve equivariance to actions of the roto-translation group SE(2). Learn about the crucial geometric and algebraic symmetries of PDE-G-CNNs, including their semiring quasilinearity, equivariance, invariance under time scaling, and isometric properties. Examine the data efficiency of these networks, observing their performance gains even with limited training data and ability to generalize to unseen test cases from different datasets. Investigate the extendability of PDE-G-CNNs to well-known convolutional architectures, focusing on a UNet variant with a new equivariant U-Net structure incorporating PDE-based morphological convolutions. Gain insights into the verification of these properties and their favorable results across various datasets.