  The success of deep learning in numerous application domains created the de-
sire to run and train them on mobile devices. This however, conflicts with
their computationally, memory and energy intense nature, leading to a growing
interest in compression. Recent work by Han et al. (2015a) propose a pipeline
that involves retraining, pruning and quantization of neural network weights,
obtaining state-of-the-art compression rates. In this paper, we show that
competitive compression rates can be achieved by using a version of soft
weight-sharing (Nowlan & Hinton, 1992). Our method achieves both quantization
and pruning in one simple (re-)training procedure. This point of view also
exposes the relation between compression and the minimum description length
(MDL) principle.
