PDE-CNNs: Axiomatic Derivations and Applications

arXiv:2403.15182v1 Announce Type: new
Abstract: 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. PDE-G-CNNs offer several key benefits all at once: fewer parameters, inherent equivariance, better performance, data efficiency, and geometric interpretability. In this article we focus on Euclidean equivariant PDE-G-CNNs where the feature maps are two dimensional throughout. We call this variant of the framework a PDE-CNN. We list several practically desirable axioms and derive from …

abstract applications article arxiv benefits cnns components convolutional neural networks cs.cv cs.lg data efficiency evolution focus interpretability key networks neural networks parameters performance type