The random deployment of small cell base stations (BSs) causes the coverage areas of neighboring cells to overlap, which increases intercell interference and degrades the system capacity. This paper proposes a new intercell interference management (IIM) scheme to improve the system capacity in multiple-input multiple-output (MIMO) small cell networks. The proposed IIM scheme consists of both an interference cancellation (IC) technique on the receiver side, and a neural network (NN) based power control algorithm for intercell interference coordination (ICIC) on the transmitter side. In order to improve the system capacity, the NN power control optimizes downlink transmit power while IC eliminates interfering signals from received signals. Computer simulations compare the system capacity of the MIMO network with several ICIC algorithms: the NN, the greedy search, the belief propagation (BP), the distributed pricing (DP), and the maximum power, all of which can be combined with IC reception. Furthermore, this paper investigates the application of a multi-layered NN structure called deep learning and its pre-training scheme, into the mobile communication field. It is shown that the performance of NN is better than that of BP and very close to that of greedy search. The low complexity of the NN algorithm makes it suitable for IIM. It is also demonstrated that combining IC and sectorization of BSs acquires high capacity gain owing to reduced interference.