Attention networks show promise for both vision and language tasks, by emphasizing relationships between constituent elements through appropriate weighting functions. Such elements could be regions in an image output by a region proposal network, or words in a sentence, represented by word embedding. Thus far, however, the learning of attention weights has been driven solely by the minimization of task specific loss functions. We here introduce a method of learning attention weights to better emphasize informative pair-wise relations between entities. The key idea is to use a novel center-mass cross entropy loss, which can be applied in conjunction with the task specific ones. We then introduce a focused attention backbone to learn these attention weights for general tasks. We demonstrate that the focused attention module leads to a new state-of-the-art for the recovery of relations in a relationship proposal task. Our experiments show that it also boosts performance for diverse vision and language tasks, including object detection, scene categorization and document classification.