Orbit recovery from invariants of low degree in representations of finite groups

Dan Edidin, Josh Katz

Session: Invariant theory for machine learning (Dustin Mixon, Soledad Villar)

Keywords: orbit recovery, finite groups

TL;DR: We study representations of finite groups for which invariants of degree at most three separate generic orbits

Abstract: Motivated by applications to equivariant neural networks and cryo-electron microscopy we consider the problem of recovering the generic orbit in a representation of a finite group from invariants of low degree. The main result proved here is that invariants of degree at most three separate generic orbits in the regular representation of a finite group defined over any infinite field. This answers a question posed in the paper {\em Estimations under group action}, by Bandeira, Blum-Smith, Kileel, Niles-Weed, Perry and Wein. We also discuss this problem for subregular reprsentations of the dihedral and symmetric groups. Other results for rotation groups will be presented in the talk.

Submission Number: 28