Empirical Remarks on the Translational Equivariance of Convolutional Layers

Abstract

In general, convolutional neural networks (CNNs) maintain some level of translational invariance. However, the convolutional layer itself is translational-equivariant. The pooling layers provide some level of invariance. In object recognition, invariance is more important than equivariance. In this paper, we investigate how vulnerable CNNs without pooling or augmentation are to translation in object recognition. For CNNs that are specialized in learning local textures but vulnerable to learning global geometric information, we propose a method to explicitly transform an image into a global feature image and then provide it as an input to neural networks. In our experiments on a modified MNIST dataset, we demonstrate that the recognition accuracy of a conventional baseline network significantly decreases from 98% to less than 60% even in the case of 2-pixel translation. We also demonstrate that the proposed method is far superior to the baseline network in terms of performance improvement.