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.

翻译：数据集通常具有其内在的对称性，而被称为等变或不变模型的特定深度学习模型已被开发用于利用这些对称性。然而，若部分或全部对称性仅为近似成立（这在实践中频繁发生），由于模型架构的限制，这些模型可能表现次优。我们针对混合对称性场景下的近似对称性问题展开研究——即数据包含多种不同类型的对称性，且各类型对称性的近似程度存在差异。与以往多数方法提出新型架构约束不同，我们提出了一种基于正则化的方法，为具有混合近似对称性的数据集构建模型。该方法的核心是面向特定对称性类型的"等变正则化项"，用于衡量模型对该类型对称性的等变程度。我们的训练过程包含多个此类正则化项（每种对称性类型对应一个），并在训练中自动调节各正则化项的强度，从而无需显式监督即可发现候选对称性类型的近似程度。通过合成函数逼近和运动预测任务，我们证明了该方法在正确发现近似对称性水平的同时，比现有方法取得了更优的精度。