Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is advantageous for robust networks to learn symmetries directly from the data to fit a task function. In this paper, we present a method to extract symmetries learned by a neural network and to evaluate the degree to which a network is invariant to them. With our method, we are able to explicitly retrieve learned invariances in a form of the generators of corresponding Lie-groups without prior knowledge of symmetries in the data. We use the proposed method to study how symmetrical properties depend on a neural network's parameterization and configuration. We found that the ability of a network to learn symmetries generalizes over a range of architectures. However, the quality of learned symmetries depends on the depth and the number of parameters.

翻译：摘要：内置于神经网络中的对称性对广泛任务极为有益，因为它节省了从数据中学习这些对称性的开销。我们从这样的立场出发：当模型未预先内置对称性时，鲁棒网络直接从数据中学习对称性以适配任务函数将具有优势。本文提出了一种方法，用于提取神经网络学习到的对称性，并评估网络对这些对称性的不变性程度。通过该方法，我们能够以对应李群生成器的形式显式地检索到学习到的不变性，而无需先验了解数据中的对称性。我们利用所提方法研究了对称性属性如何依赖于神经网络的参数化与配置。研究发现，网络学习对称性的能力在不同架构中具有泛化性，但学习到的对称性质量则取决于网络的深度与参数数量。