  In this paper, we propose quantized densely connected U-Nets for efficient
visual landmark localization. The idea is that features of the same semantic
meanings are globally reused across the stacked U-Nets. This dense connectivity
largely improves the information flow, yielding improved localization accuracy.
However, a vanilla dense design would suffer from critical efficiency issue in
both training and testing. To solve this problem, we first propose order-K
dense connectivity to trim off long-distance shortcuts; then, we use a
memory-efficient implementation to significantly boost the training efficiency
and investigate an iterative refinement that may slice the model size in half.
Finally, to reduce the memory consumption and high precision operations both in
training and testing, we further quantize weights, inputs, and gradients of our
localization network to low bit-width numbers. We validate our approach in two
tasks: human pose estimation and face alignment. The results show that our
approach achieves state-of-the-art localization accuracy, but using ~70% fewer
parameters, ~98% less model size and saving ~75% training memory compared with
other benchmark localizers. The code is available at
https://github.com/zhiqiangdon/CU-Net.
