This paper studies a deep learning approach for binary assignment problems in wireless networks, which identifies binary variables for permutation matrices. This poses challenges in designing a structure of a neural network and its training strategies for generating feasible assignment solutions. To this end, this paper develop a new Sinkhorn neural network which learns a non-convex projection task onto a set of permutation matrices. An unsupervised training algorithm is proposed where the Sinkhorn neural network can be applied to network assignment problems. Numerical results demonstrate the effectiveness of the proposed method in various network scenarios.