An ensemble of neural networks is known to be more robust and accurate than an individual network, however usually with linearly-increased cost in both training and testing. 
 In this work, we propose a two-stage method to learn Sparse Structured Ensembles (SSEs) for neural networks.
 In the first stage, we run SG-MCMC with group sparse priors to draw an ensemble of samples from the posterior distribution of network parameters. In the second stage, we apply weight-pruning to each sampled network and then perform retraining over the remained connections.
 In this way of learning SSEs with SG-MCMC and pruning, we not only achieve high prediction accuracy since SG-MCMC enhances exploration of the model-parameter space, but also reduce memory and computation cost significantly in both training and testing of NN ensembles.
 This is thoroughly evaluated in the experiments of learning SSE ensembles of both FNNs and LSTMs.
 For example, in LSTM based language modeling (LM), we obtain 21\% relative reduction in LM perplexity by learning a SSE of 4 large LSTM models, which has only 30\% of model parameters and 70\% of computations in total, as compared to the baseline large LSTM LM.
 To the best of our knowledge, this work represents the first methodology and empirical study of integrating SG-MCMC, group sparse prior and network pruning together for learning NN ensembles.
Propose a novel method by integrating SG-MCMC sampling, group sparse prior and network pruning to learn Sparse Structured Ensemble (SSE) with improved performance and significantly reduced cost than traditional methods.  The authors propose a procedure to generate an ensemble of sparse structured models A new framework for training ensemble neural networks that uses SG-MCMC methods within deep learning, and then increases computational efficiency by group sparsity+pruning. This paper explores the use of FNN and LSTMs to make bayesian model averaging more computationally feasible and improve average model performance.