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.

通过研究发现，即使强制施加不完全匹配于领域对称性的equivariance约束，也能显著提高机器学习环境中对真实对称性的学习效率和性能。在强制施加extrinsic symmetry的情况下，在具有潜在对称性的领域中，equivariant model的表现优于non-equivariant方法。

在具有潜在对称性的领域中，等变模型的惊人有效性