  We present LBW-Net, an efficient optimization based method for quantization
and training of the low bit-width convolutional neural networks (CNNs).
Specifically, we quantize the weights to zero or powers of two by minimizing
the Euclidean distance between full-precision weights and quantized weights
during backpropagation. We characterize the combinatorial nature of the low
bit-width quantization problem. For 2-bit (ternary) CNNs, the quantization of
$N$ weights can be done by an exact formula in $O(N\log N)$ complexity. When
the bit-width is three and above, we further propose a semi-analytical
thresholding scheme with a single free parameter for quantization that is
computationally inexpensive. The free parameter is further determined by
network retraining and object detection tests. LBW-Net has several desirable
advantages over full-precision CNNs, including considerable memory savings,
energy efficiency, and faster deployment. Our experiments on PASCAL VOC dataset
show that compared with its 32-bit floating-point counterpart, the performance
of the 6-bit LBW-Net is nearly lossless in the object detection tasks, and can
even do better in some real world visual scenes, while empirically enjoying
more than 4$\times$ faster deployment.
