Title: Automatic Parameter Tying in Neural Networks. Abstract: Recently, there has been growing interest in methods that perform neural network compression, namely techniques that attempt to substantially reduce the size of a neural network without significant reduction in performance. However, most existing methods are post-processing approaches in that they take a learned neural network as input and output a compressed network by either forcing several parameters to take the same value (parameter tying via quantization) or pruning irrelevant edges (pruning) or both. In this paper, we propose a novel algorithm that jointly learns and compresses a neural network. The key idea in our approach is to change the optimization criteria by adding $k$ independent Gaussian priors over the parameters and a sparsity penalty. We show that our approach is easy to implement using existing neural network libraries, generalizes L1 and L2 regularization and elegantly enforces parameter tying as well as pruning constraints. Experimentally, we demonstrate that our new algorithm yields state-of-the-art compression on several standard benchmarks with minimal loss in accuracy while requiring little to no hyperparameter tuning as compared with related, competing approaches. 