Techniques for statistics-aware weight quantization are presented. To facilitate reducing the bit precision of weights, for a set of weights, a quantizer management component can estimate a quantization scale value to apply to a weight as a linear or non-linear function of the mean of a square of a weight value of the weight and the mean of an absolute value of the weight value, wherein the quantization scale value is determined to have a smaller quantization error than all, or at least almost all, other quantization errors associated with other quantization scale values. A quantizer component applies the quantization scale value to symmetrically and/or uniformly quantize weights of a layer of the set of weights to generate quantized weights, the weights being quantized using rounding. The respective quantized weights can be used to facilitate training and inference of a deep learning system.