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Datasets often have their intrinsic symmetries, and particular deep-learningmodels called equivariant or invariant models have been developed to exploitthese symmetries. However, if some or all of these symmetries are onlyapproximate, which frequently happens in practice, these models may besuboptimal due to the architectural restrictions imposed on them. We tacklethis issue of approximate symmetries in a setup where symmetries are mixed,i.e., they are symmetries of not single but multiple different types and thedegree of approximation varies across these types. Instead of proposing a newarchitectural restriction as in most of the previous approaches, we present aregularizer-based method for building a model for a dataset with mixedapproximate symmetries. The key component of our method is what we callequivariance regularizer for a given type of symmetries, which measures howmuch a model is equivariant with respect to the symmetries of the type. Ourmethod is trained with these regularizers, one per each symmetry type, and thestrength of the regularizers is automatically tuned during training, leading tothe discovery of the approximation levels of some candidate symmetry typeswithout explicit supervision. Using synthetic function approximation and motionforecasting tasks, we demonstrate that our method achieves better accuracy thanprior approaches while discovering the approximate symmetry levels correctly.

Regularizing Towards Soft Equivariance Under Mixed Symmetries