A Unified Framework for Discovering Discrete Symmetries
This addresses the challenge of symmetry discovery in machine learning, which is incremental as it builds on existing methods for specific symmetry types.
The paper tackles the problem of learning functions that respect symmetries from a class of subgroups, developing a unified framework that discovers symmetries like locally symmetric, dihedral, and cyclic subgroups, with experiments on image-digit sum and polynomial regression tasks showing its effectiveness.
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear, matrix-valued and non-linear functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the non-linear functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the matrix-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.