Learning Sparse Structured Ensembles with SG-MCMC and Network Pruning
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.
 The authors note that several recent papers have shown that bayesian model averaging is an effective and universal way to improve hold-out performance, but unfortunately are limited by increased computational costs. Towards that end, the authors of this manuscript propose several modifications to this procedure to make it computationally feasible and indeed improve performance. Pros: The authors demonstrate an effective procedure for FNN and LSTMs that makes model averaging improve performance. Empirical evidence is convincing on the utility of the approach. Cons: Not clear how this approach would be used with convolutional structures Much of the benefit appears to come from the sparse prior, pruning, and retraining (Figure 3). The model averaging seems to have a smaller contribution. Due to that, it seems that the nature of the contribution needs to be clarified compared to the large literature on sparsifying neural networks, and the introductory comments of the paper should be rewritten to reflect that reality.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Sparse Structured Ensembles with SG-MCMC and Network Pruning
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.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The authors note that several recent papers have shown that bayesian model averaging is an effective and universal way to improve hold-out performance, but unfortunately are limited by increased computational costs. Towards that end, the authors of this manuscript propose several modifications to this procedure to make it computationally feasible and indeed improve performance. Pros: The authors demonstrate an effective procedure for FNN and LSTMs that makes model averaging improve performance. Empirical evidence is convincing on the utility of the approach. Cons: Not clear how this approach would be used with convolutional structures Much of the benefit appears to come from the sparse prior, pruning, and retraining (Figure 3). The model averaging seems to have a smaller contribution. Due to that, it seems that the nature of the contribution needs to be clarified compared to the large literature on sparsifying neural networks, and the introductory comments of the paper should be rewritten to reflect that reality.
assistant
 The authors note that several recent papers have shown that bayesian model averaging is an effective and universal way to improve hold-out performance, but unfortunately are limited by increased computational costs. Towards that end, the authors of this manuscript propose several modifications to this procedure to make it computationally feasible and indeed improve performance. Pros: The authors demonstrate an effective procedure for FNN and LSTMs that makes model averaging improve performance. Empirical evidence is convincing on the utility of the approach. Cons: Not clear how this approach would be used with convolutional structures Much of the benefit appears to come from the sparse prior, pruning, and retraining (Figure 3). The model averaging seems to have a smaller contribution. Due to that, it seems that the nature of the contribution needs to be clarified compared to the large literature on sparsifying neural networks, and the introductory comments of the paper should be rewritten to reflect that reality.