  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.
