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：神经网络对几何变换的等变性可提升数据效率、参数效率及对域外视角偏移的鲁棒性。当等变性未被显式设计到网络中时，网络仍能从数据中学习等变函数。我们通过提出一种改进的等变性度量方法对此类学到的等变性进行量化。研究发现，在ImageNet数据集上，学到的平移等变性与验证精度之间存在相关性。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，结果表明数据增强、降低模型容量以及卷积形式的归纳偏置均能有效提升神经网络中学习到的等变性。