Data augmentation is used in machine learning to make the classifier invariant to label-preserving transformations. Usually this invariance is only encouraged implicitly by including a single augmented input during training. However, several works have recently shown that using multiple augmentations per input can improve generalisation or can be used to incorporate invariances more explicitly. In this work, we first empirically compare these recently proposed objectives that differ in whether they rely on explicit or implicit regularisation and at what level of the predictor they encode the invariances. We show that the predictions of the best performing method are also the most similar when compared on different augmentations of the same input. Inspired by this observation, we propose an explicit regulariser that encourages this invariance on the level of individual model predictions. Through extensive experiments on CIFAR-100 and ImageNet we show that this explicit regulariser (i) improves generalisation and (ii) equalises performance differences between all considered objectives. Our results suggest that objectives that encourage invariance on the level of the neural network itself generalise better than those that achieve invariance by averaging predictions of non-invariant models.

When seeing a new object, humans can immediately recognize it across different retinal locations: the internal object representation is invariant to translation. It is commonly believed that Convolutional Neural Networks (CNNs) are architecturally invariant to translation thanks to the convolution and/or pooling operations they are endowed with. In fact, several studies have found that these networks systematically fail to recognise new objects on untrained locations. In this work, we test a wide variety of CNNs architectures showing how, apart from DenseNet-121, none of the models tested was architecturally invariant to translation. Nevertheless, all of them could learn to be invariant to translation. We show how this can be achieved by pretraining on ImageNet, and it is sometimes possible with much simpler data sets when all the items are fully translated across the input canvas. At the same time, this invariance can be disrupted by further training due to catastrophic forgetting/interference. These experiments show how pretraining a network on an environment with the right `latent' characteristics (a more naturalistic environment) can result in the network learning deep perceptual rules which would dramatically improve subsequent generalization.