Title: Learning Multi-Object Positional Relationships via Emergent Communication. Abstract: The study of emergent communication has been dedicated to interactive artificial intelligence. While existing work focuses on communication about single objects or complex image scenes, we argue that communicating relationships between multiple objects is important in more realistic tasks, but understudied. In this paper, we try to fill this gap and focus on emergent communication about positional relationships between two objects. We train agents in the referential game where observations contain two objects, and find that generalization is the major problem when the positional relationship is involved. The key factor affecting the generalization ability of the emergent language is the input variation between Speaker and Listener, which is realized by a random image generator in our work. Further, we find that the learned language can generalize well in a new multi-step MDP task where the positional relationship describes the goal, and performs better than raw-pixel images as well as pre-trained image features, verifying the strong generalization ability of discrete sequences. We also show that language transfer from the referential game performs better in the new task than learning language directly in this task, implying the potential benefits of pre-training in referential games. All in all, our experiments demonstrate the viability and merit of having agents learn to communicate positional relationships between multiple objects through emergent communication.