We analyze the trade-off between quantization noise and clipping distortion in low precision networks. We identify the statistics of various tensors, and derive exact expressions for the mean-square-error degradation due to clipping. By optimizing these expressions, we show marked improvements over standard quantization schemes that normally avoid clipping. For example, just by choosing the accurate clipping values, more than 40\% accuracy improvement is obtained for the quantization of VGG-16 to 4-bits of precision. Our results have many applications for the quantization of neural networks at both training and inference time. 

We analyze the trade-off between quantization noise and clipping distortion in low precision networks, and show marked improvements over standard quantization schemes that normally avoid clipping Derives a formula for finding the minimum and maximum clipping values for uniform quantization which minimize the square error resulting from quantization, for either a Laplace or Gaussian distribution over pre-quantized value.