Equivariant Representations for Non-Free Group Actions

01/12/2023
by   Luis Armando Pérez Rey, et al.
0

We introduce a method for learning representations that are equivariant with respect to general group actions over data. Differently from existing equivariant representation learners, our method is suitable for actions that are not free i.e., that stabilize data via nontrivial symmetries. Our method is grounded in the orbit-stabilizer theorem from group theory, which guarantees that an ideal learner infers an isomorphic representation. Finally, we provide an empirical investigation on image datasets with rotational symmetries and show that taking stabilizers into account improves the quality of the representations.

READ FULL TEXT
research
07/07/2022

Equivariant Representation Learning via Class-Pose Decomposition

We introduce a general method for learning representations that are equi...
research
07/25/2022

Homomorphism Autoencoder – Learning Group Structured Representations from Observed Transitions

How can we acquire world models that veridically represent the outside w...
research
07/22/2023

Quantum Money from Abelian Group Actions

We give a candidate construction of public key quantum money, and even a...
research
01/04/2023

Cryptographic Group and Semigroup Actions

We consider actions of a group or a semigroup on a set, which generalize...
research
07/23/2019

Pre-Learning Environment Representations for Data-Efficient Neural Instruction Following

We consider the problem of learning to map from natural language instruc...
research
03/11/2009

Free actions and Grassmanian variety

An algebraic notion of representational consistency is defined. A theore...
research
05/13/2019

Group Re-identification via Transferred Single and Couple Representation Learning

Group re-identification (G-ReID) is an important yet less-studied task. ...

Please sign up or login with your details

Forgot password? Click here to reset