Abstract: Affinity graphs are widely used in deep architectures, including graph convolutional neural networks and attention networks. Thus far, the literature has focused on abstracting features from such graphs, while the learning of the affinities themselves has been overlooked. Here we propose a principled method to directly supervise the learning of weights in affinity graphs, to exploit meaningful connections between entities in the data source. Applied to a visual attention network, our affinity supervision improves relationship recovery between objects, even without the use of manually annotated relationship labels. We further show that affinity learning between objects boosts scene categorization performance and that the supervision of affinity can also be applied to graphs built from mini-batches, for neural network training. In an image classification task we demonstrate consistent improvement over the baseline, with diverse network architectures and datasets.