  Efficient model inference is an important and practical issue in the
deployment of deep neural network on resource constraint platforms. Network
quantization addresses this problem effectively by leveraging low-bit
representation and arithmetic that could be conducted on dedicated embedded
systems. In the previous works, the parameter bitwidth is set homogeneously and
there is a trade-off between superior performance and aggressive compression.
Actually the stacked network layers, which are generally regarded as
hierarchical feature extractors, contribute diversely to the overall
performance. For a well-trained neural network, the feature distributions of
different categories differentiate gradually as the network propagates forward.
Hence the capability requirement on the subsequent feature extractors is
reduced. It indicates that the neurons in posterior layers could be assigned
with lower bitwidth for quantized neural networks. Based on this observation, a
simple but effective mixed-precision quantized neural network with
progressively ecreasing bitwidth is proposed to improve the trade-off between
accuracy and compression. Extensive experiments on typical network
architectures and benchmark datasets demonstrate that the proposed method could
achieve better or comparable results while reducing the memory space for
quantized parameters by more than 30\% in comparison with the homogeneous
counterparts. In addition, the results also demonstrate that the
higher-precision bottom layers could boost the 1-bit network performance
appreciably due to a better preservation of the original image information
while the lower-precision posterior layers contribute to the regularization of
$k-$bit networks.
