Title: Efficient generation of structured objects with Constrained Adversarial Networks. Abstract: Despite their success, generative adversarial networks (GANs) cannot easily generate structured objects like molecules or game maps. The issue is that such objects must satisfy structural requirements (e.g., molecules must be chemically valid, game maps must guarantee reachability of the end goal) that are difficult to capture with examples alone.  As a remedy, we     propose constrained adversarial networks (CANs), which embed the constraints into the model during training by penalizing the generator whenever it outputs invalid structures. As in unconstrained GANs, new objects can be sampled straightforwardly from the generator, but in addition they satisfy the constraints with high probability.  Our approach handles arbitrary logical constraints and leverages knowledge compilation techniques to efficiently evaluate the expected disagreement between the     model and the constraints.  This setup is further extended to hybrid logical-neural constraints for capturing complex requirements like graph reachability.  An extensive empirical analysis on constrained images, molecules, and video game levels shows that CANs efficiently generate valid structures that are both high-quality and novel.