The optimal scheduling of interfering links in a dense wireless network with full frequency reuse is a challenging task. The traditional method involves first estimating all the interfering channel strengths then optimizing the scheduling based on the model. This model-based method is however resource intensive and computationally hard, because channel estimation is expensive in dense networks; further, finding even a locally optimal solution of the resulting optimization problem may be computationally complex. This paper shows that by using a deep learning approach, it is possible to bypass channel estimation and to schedule links efficiently based solely on the geographic locations of transmitters and receivers for networks in which the channels are largely functions of distance dependent path-losses. This is accomplished by unsupervised training over randomly deployed networks, and by using a novel neural network architecture that takes the geographic spatial convolutions of the interfering or interfered neighboring nodes as input over multiple feedback stages to learn the optimum solution. The resulting neural network gives near-optimal performance for sum-rate maximization and is capable of generalizing to larger deployment areas and to deployments of different link densities. Moreover, to provide fairness, this paper proposes a novel scheduling approach that utilizes the sum-rate optimal scheduling algorithm over judiciously chosen subsets of links for maximizing a proportional fairness objective over the network. The proposed approach shows highly competitive and generalizable network utility maximization results.