A revisit to MacKay algorithm and its application to deep network compression An iterative procedure introduced in MacKayxe2x80x99s evidence framework is often used for estimating the hyperparameter in empirical Bayes. Together with the use of a particular form of prior, the estimation of the hyperparameter reduces to an automatic relevance determination model, which provides a soft way of pruning model parameters. Despite the effectiveness of this estimation procedure, it has stayed primarily as a heuristic to date and its application to deep neural network has not yet been explored. This paper formally investigates the mathematical nature of this procedure and justifies it as a wellprincipled algorithm framework, which we call the MacKay algorithm. As an application, we demonstrate its use in deep neural networks, which have typically complicated structure with millions of parameters and can be pruned to reduce the memory requirement and boost computational efficiency. In experiments, we adopt MacKay algorithm to prune the parameters of both simple networks such as LeNet, deep convolution VGGlike networks, and residual netowrks for large image classification task. Experimental results show that the algorithm can compress neural networks to a high level of sparsity with little loss of prediction accuracy, which is comparable with the stateoftheart.

A Unified Approximation Framework for Compressing and Accelerating Deep Neural Networks Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model size and the intensive computation. To address this issue, various approximation techniques have been investigated, which seek for a light weighted network with little performance degradation in exchange of smaller model size or faster inference. Both lowrankness and sparsity are appealing properties for the network approximation. In this paper we propose a unified framework to compress the convolutional neural networks (CNNs) by combining these two properties, while taking the nonlinear activation into consideration. Each layer in the network is approximated by the sum of a structured sparse component and a lowrank component, which is formulated as an optimization problem. Then, an extended version of alternating direction method of multipliers (ADMM) with guaranteed convergence is presented to solve the relaxed optimization problem. Experiments are carried out on VGG16, AlexNet and GoogLeNet with large image classification datasets. The results outperform previous work in terms of accuracy degradation, compression rate and speedup ratio. The proposed method is able to remarkably compress the model (with up to 4.9X reduction of parameters) at a cost of little loss or without loss on accuracy.