A Unified Framework for Discovering Discrete Symmetries
- URL: http://arxiv.org/abs/2309.02898v2
- Date: Fri, 27 Oct 2023 09:24:20 GMT
- Title: A Unified Framework for Discovering Discrete Symmetries
- Authors: Pavan Karjol, Rohan Kashyap, Aditya Gopalan, Prathosh A.P
- Abstract summary: 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.
- Score: 17.687122467264487
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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