Content-invariance in mapping codes learned by GAEs is a useful feature for various relation learning tasks. In this paper we show that the content-invariance of mapping codes for images of 2D and 3D rotated objects can be substantially improved by extending the standard GAE loss (symmetric reconstruction error) with a regularization term that penalizes the symmetric cross-reconstruction error. This error term involves reconstruction of pairs with mapping codes obtained from other pairs exhibiting similar transformations. Although this would principally require knowledge of the transformations exhibited by training pairs, our experiments show that a bootstrapping approach can sidestep this issue, and that the regularization term can effectively be used in an unsupervised setting.