Title: Global-Local Network for Learning Depth with Very Sparse Supervision. Abstract: Natural intelligent agents learn to perceive the three dimensional structure of the world without training on large datasets and are unlikely to have the precise equations of projective geometry hard-wired in the brain. Such skill would also be  valuable  to  artificial  systems  in  order  to  avoid  the  expensive  collection  of labeled datasets, as well as tedious tuning required by methods based on multi-view geometry. Inspired by natural agents, who interact with the environment via visual and haptic feedback, this paper explores a new approach to learning depth from images and very sparse depth measurements, just a few pixels per image. To learn from such extremely sparse supervision, we introduce an appropriate inductive bias by designing a specialized global-local network architecture. Experiments on several datasets show that the proposed model can learn monocular dense depth estimation when trained with very sparse ground truth, even a single pixel per image. Moreover, we find that the global parameters extracted by the network are predictive of the metric agent motion.