Interference alignment (IA) is a linear precoding strategy that can achieve optimal capacity scaling at high SNR in interference networks. Most of the existing IA designs require full channel state information (CSI) at the transmitters, which induces a huge CSI signaling cost. Hence it is desirable to improve the feedback efficiency for IA and in this paper, we propose a novel IA scheme with a significantly reduced CSI feedback. To quantify the CSI feedback cost, we introduce a novel metric, namely the feedback dimension. This metric serves as a first-order measurement of CSI feedback overhead. Due to the partial CSI feedback constraint, conventional IA schemes can not be applied and hence, we develop a novel IA precoder / decorrelator design and establish new IA feasibility conditions. Via dynamic feedback profile design, the proposed IA scheme can also achieve a flexible tradeoff between the degree of freedom (DoF) requirements for data streams, the antenna resources and the CSI feedback cost. We show by analysis and simulations that the proposed scheme achieves substantial reductions of CSI feedback overhead under the same DoF requirement in MIMO interference networks.