In frequency division duplex (FDD) multiple-input multiple-output (MIMO) wireless communications, limited channel state information (CSI) feedback is a central tool to support advanced single- and multi-user MIMO beamforming/precoding. To achieve a given CSI quality, the CSI quantization codebook size has to grow exponentially with the number of antennas, leading to quantization complexity, as well as, feedback overhead issues for larger MIMO systems. We have recently proposed a multi-stage recursive Grassmannian quantizer that enables a significant complexity reduction of CSI quantization. In this paper, we show that this recursive quantizer can effectively be combined with deep learning classification to further reduce the complexity, and that it can exploit temporal channel correlations to reduce the CSI feedback overhead.