Employing equivariance in neural networks leads to greater parameter
efficiency and improved generalization performance through the encoding of
domain knowledge in the architecture; however, the majority of existing
approaches require an a priori specification of the desired symmetries. We
present a neural network architecture, Linear Group Networks (LGNs), for
learning linear groups acting on the weight space of neural networks. Linear
groups are desirable due to their inherent interpretability, as they can be
represented as finite matrices. LGNs learn groups without any supervision or
knowledge of the hidden symmetries in the data and the groups can be mapped to
well known operations in machine learning. We use LGNs to learn groups on
multiple datasets while considering different downstream tasks; we demonstrate
that the linear group structure depends on both the data distribution and the
considered task.

本文介绍了一种神经网络的架构 —— 线性群网络 (LGNs)，其不需要提前规定对称性，在不需要监督或知道数据中隐藏的对称性的情况下，学习作用于神经网络权值空间上的线性群，并且可映射到机器学习中的已知操作。我们使用 LGNs 在多个数据集上学习群，并考虑不同的下游任务。结果表明，线性群结构取决于数据分布和所考虑的任务。