  Quantizing deep convolutional neural networks for image super-resolution
substantially reduces their computational costs. However, existing works either
suffer from a severe performance drop in ultra-low precision of 4 or lower
bit-widths, or require a heavy fine-tuning process to recover the performance.
To our knowledge, this vulnerability to low precisions relies on two
statistical observations of feature map values. First, distribution of feature
map values varies significantly per channel and per input image. Second,
feature maps have outliers that can dominate the quantization error. Based on
these observations, we propose a novel distribution-aware quantization scheme
(DAQ) which facilitates accurate training-free quantization in ultra-low
precision. A simple function of DAQ determines dynamic range of feature maps
and weights with low computational burden. Furthermore, our method enables
mixed-precision quantization by calculating the relative sensitivity of each
channel, without any training process involved. Nonetheless, quantization-aware
training is also applicable for auxiliary performance gain. Our new method
outperforms recent training-free and even training-based quantization methods
to the state-of-the-art image super-resolution networks in ultra-low precision.
