Equivariance w.r.t. geometric transformations in neural networks improves data efficiency, parameter efficiency and robustness to out-of-domain perspective shifts. When equivariance is not designed into a neural network, the network can still learn equivariant functions from the data. We quantify this learned equivariance, by proposing an improved measure for equivariance. We find evidence for a correlation between learned translation equivariance and validation accuracy on ImageNet. We therefore investigate what can increase the learned equivariance in neural networks, and find that data augmentation, reduced model capacity and inductive bias in the form of convolutions induce higher learned equivariance in neural networks.

翻译：神经网络相对于几何变换的等变性能够提升数据效率、参数效率以及对域外视角变化的鲁棒性。当等变性未被显式设计到神经网络中时，网络仍能从数据中学习到等变函数。我们通过提出一种改进的等变性度量方法，对这类学习到的等变性进行了量化分析。研究发现，在ImageNet数据集上，学习到的平移等变性与验证准确率之间存在相关性。为此，我们进一步探究了增强神经网络中学习到的等变性的因素，发现数据增强、降低模型容量以及卷积形式的归纳偏差能够促使神经网络获得更高的学习等变性。