Equivariant Filters are Equivariant

Learning Steerable Filters for Rotation Equivariant CNNs

In many machine learning tasks it is desirable that a model’s prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equi...

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

Equivariant Completion

The purpose of this sequel to [5] is to construct and characterize completions of G-spaces, where G is a compact Lie group. We assume the notations and results of [5]. It is a pleasure to thank Pete Bousfield for the proof of Lemma 12. Since completions are less generally familiar than localizations, a quick summary of the relevant part of the nonequivariant theory is in order. We are intereste...

Equivariant Localization

The purpose of this note is to construct and characterize localizations of G-spaces, where G is a compact Lie group. It was written at the request of Reinhard Schultz, who needed its results in work of his own. When G is finite, the possibility of such a construction is folklore familiar to the experts. That the general case presents little more difficulty comes as something of a surprise. Of c...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology