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.

翻译：我们考虑从一类对称性中学习遵循某种对称性的函数问题。我们开发了一个统一框架，能够在包括局部对称子群、二面体子群和循环子群在内的广泛子群类别中实现对称性发现。该框架的核心是一种由线性函数和张量值函数组成的新型架构，能够以有原则的方式表达对这些子群不变的函数。该架构的结构使我们能够分别利用多臂老虎机算法和梯度下降法高效优化线性函数和张量值函数，并推断最终学习到的对称性。我们还讨论了架构中张量值函数的必要性。在图像数字求和与多项式回归任务上的实验证明了我们方法的有效性。