Regularizing Towards Soft Equivariance Under Mixed Symmetries
This work addresses the challenge of building models for datasets with mixed approximate symmetries, which is a common issue in practice, offering a flexible alternative to rigid architectural restrictions.
The paper tackles the problem of approximate symmetries in datasets, where symmetries are mixed and vary in approximation levels, by introducing a regularizer-based method that automatically tunes regularization strength during training. The method achieves better accuracy than prior approaches and correctly discovers approximate symmetry levels in synthetic function approximation and motion forecasting tasks.
Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate, which frequently happens in practice, these models may be suboptimal due to the architectural restrictions imposed on them. We tackle this issue of approximate symmetries in a setup where symmetries are mixed, i.e., they are symmetries of not single but multiple different types and the degree of approximation varies across these types. Instead of proposing a new architectural restriction as in most of the previous approaches, we present a regularizer-based method for building a model for a dataset with mixed approximate symmetries. The key component of our method is what we call equivariance regularizer for a given type of symmetries, which measures how much a model is equivariant with respect to the symmetries of the type. Our method is trained with these regularizers, one per each symmetry type, and the strength of the regularizers is automatically tuned during training, leading to the discovery of the approximation levels of some candidate symmetry types without explicit supervision. Using synthetic function approximation and motion forecasting tasks, we demonstrate that our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.