  In many machine learning applications, labeled data is scarce and obtaining
more labels is expensive. We introduce a new approach to supervising neural
networks by specifying constraints that should hold over the output space,
rather than direct examples of input-output pairs. These constraints are
derived from prior domain knowledge, e.g., from known laws of physics. We
demonstrate the effectiveness of this approach on real world and simulated
computer vision tasks. We are able to train a convolutional neural network to
detect and track objects without any labeled examples. Our approach can
significantly reduce the need for labeled training data, but introduces new
challenges for encoding prior knowledge into appropriate loss functions.
