A Semantic Loss Function for Deep Learning Under Weak Supervision∗

This paper develops a novel methodology for using symbolic knowledge in deep learning. We define a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that our semantic loss function effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects under weak supervision, such as rankings and shortest paths.