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 and tensor-valued 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
tensor-valued functions, respectively, and to infer the symmetry that is
ultimately learnt. We also discuss the necessity of the tensor-valued functions
in the architecture. Experiments on image-digit sum and polynomial regression
tasks demonstrate the effectiveness of our approach.

我们开发了一个统一的框架，通过线性和张量值函数的组合表达在各种子群中对称不变的函数，利用多臂老虎机算法和梯度下降优化线性和张量值函数，从而学习出对应的对称性。通过图像数字求和和多项式回归任务的实验，证明了我们方法的有效性。