Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain symmetry is fully described by explicit transformations of the model inputs and outputs. However, many real-life applications contain only latent or partial symmetries which cannot be easily described by simple transformations of the input. In these cases, it is necessary to learn symmetry in the environment instead of imposing it mathematically on the network architecture. We discover, surprisingly, that imposing equivariance constraints that do not exactly match the domain symmetry is very helpful in learning the true symmetry in the environment. We differentiate between extrinsic and incorrect symmetry constraints and show that while imposing incorrect symmetry can impede the model's performance, imposing extrinsic symmetry can actually improve performance. We demonstrate that an equivariant model can significantly outperform non-equivariant methods on domains with latent symmetries both in supervised learning and in reinforcement learning for robotic manipulation and control problems.

翻译：大量研究表明，通过在网络架构中施加归纳偏置，等变神经网络能显著提升样本效率与泛化能力。这些应用通常假设领域对称性可通过模型输入输出的显式变换完全描述。然而，许多实际应用仅包含隐式或部分对称性，难以通过简单的输入变换加以描述。在此类情形中，需要在环境中学习对称性，而非将对称性以数学方式强加于网络架构。我们意外发现，施加与领域对称性不完全匹配的等变约束，竟能极大促进对环境真实对称性的学习。我们区分了外在对称约束与错误对称约束，并表明：错误对称约束会阻碍模型性能，而外在对称约束反而能提升性能。我们证明，在包含隐对称性的领域（包括监督学习及机器人操作与控制问题的强化学习场景）中，等变模型可显著优于非等变方法。