Abstract Semantic sparsity is a common challenge in structured visual classification problems; when the output space is complex, the vast majority of the possible predictions are rarely, if ever, seen in the training set. This paper studies semantic sparsity in situation recognition, the task of producing structured summaries of what is happening in images, including activities, objects and the roles objects play within the activity. For this problem, we find empirically that most substructures required for prediction are rare, and current state-of-the-art model performance dramatically decreases if even one such rare substructure exists in the target output.We avoid many such errors by (1) introducing a novel tensor composition function that learns to share examples across substructures more effectively and (2) semantically augmenting our training data with automatically gathered examples of rarely observed outputs using web data. When integrated within a complete CRF-based structured prediction model, the tensor-based approach outperforms existing state of the art by a relative improvement of 2.11% and 4.40% on top-5 verb and noun-role accuracy, respectively. Adding 5 million images with our semantic augmentation techniques gives further relative improvements of 6.23% and 9.57% on top-5 verb and noun-role accuracy