Machine learning models have achieved human-level performance on various tasks. This success comes at a high cost of computation and storage overhead, which makes machine learning algorithms difficult to deploy on edge devices. Typically, one has to partially sacrifice accuracy in favor of an increased performance quantified in terms of reduced memory usage and energy consumption. Current methods compress the networks by reducing the precision of the parameters or by eliminating redundant ones. In this paper, we propose a new insight into network compression through the Bayesian framework. We show that Bayesian neural networks automatically discover redundancy in model parameters, thus enabling self-compression, which is linked to the propagation of uncertainty through the layers of the network. Our experimental results show that the network architecture can be successfully compressed by deleting parameters identified by the network itself while retaining the same level of accuracy.