标题： 在混合对称性下的软等变性正则化 显示英文标题

标题： Regularizing Towards Soft Equivariance Under Mixed Symmetries

摘要： 数据集通常具有其内在对称性，已经开发出称为等变或不变的深度学习模型来利用这些对称性。 然而，如果这些对称性只是近似的，这在实践中经常发生，由于对模型施加的结构限制，这些模型可能会次优。 我们在一种对称性混合的情况下解决近似对称性的问题，即这些对称性不是单一类型而是多种不同类型，并且这些类型的近似程度各不相同。 我们没有像大多数先前方法那样提出新的结构限制，而是提出了一种基于正则化的方法，用于构建具有混合近似对称性的数据集的模型。 我们方法的关键组成部分是我们称之为给定类型对称性的等变正则化器，它衡量模型相对于该类型对称性的等变程度。 我们的方法使用这些正则化器进行训练，每个对称性类型一个正则化器，正则化器的强度在训练过程中自动调整，从而在没有显式监督的情况下发现某些候选对称性类型的近似水平。 通过合成函数逼近和运动预测任务，我们证明了我们的方法在正确发现近似对称性水平的同时，比之前的方法取得了更好的准确性。 显示英文摘要

摘要： 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.