Soft Weight-Sharing for Neural Network Compression
The success of deep learning in numerous application domains created the desire to run and train them on mobile devices. This however, conflicts with their computationally, memory and energy intense nature, leading to a growing interest in compression. Recent work by Han et al. (2016) propose a pipeline that involves retraining, pruning and quantization of neural network weights, obtaining state-of-the-art compression rates. In this paper, we show that competitive compression rates can be achieved by using a version of *soft weight-sharing* (Nowlan & Hinton, 1991). Our method achieves both quantization and pruning in one simple (re-)training procedure. This point of view also exposes the relation between compression and the minimum description length (MDL) principle.
This paper proposes to use an empirical Bayesian approach to learn the parameters of a neural network, and their priors. A mixture model prior over the weights leads to a clustering effect in the weight posterior distributions (which are approximated with delta peaks). This clustering effect can exploited for parameter quantisation and compression of the network parameters. The authors show that this leads to compression rates and predictive accuracy comparable to related approaches. Earlier work [Han et al. 2015] is based on a three-stage process of pruning small magnitude weights, clustering the remaining ones, and updating the cluster centres to optimise performance. The current work provides a more principled approach that does not have such an ad-hoc multi-stage structure, but a single iterative optimisation process. A first experiment, described in section 6.1 shows that an empirical Bayes’ approach, without the use of hyper priors, already leads to a pronounced clustering effect and to setting many weights to zero. In particular a compression rate of 64.2 is obtained on the LeNet300-100 model. In section 6.1 the text refers to figure C, I suppose this should be figure 1. Section 6.2 describes an experiment where hyper-priors are used, and the parameters of these distributions, as well as other hyper-parameters such as the learning rates, are being optimised using Spearmint (Snoek et al., 2012). Figure 2 shows the performance of the different points in the hyper-parameter space that have been evaluated (each trained network gives an accuracy-compressionrate point in the graph). The text claims that best results lie on a line, this seems a little opportunistic interpretation given the limited data. Moreover, it would be useful to add a small discussion on whether such a linear relationship would be expected or not. Currently the results of this experiment lack interpretation. Section 6.3 describes results obtained for both CNN models and compares results to the recent results of (Han et al., 2015) and (Guo et al., 2016). Comparable results are obtained in terms of compression rate and accuracy. The authors state that their current algorithm is too slow to be useful for larger models such as VGG-19, but they do briefly report some results obtained for this model (but do not compare to related work). It would be useful here to explain what slows the training down with respect to standard training without the weight clustering approach, and how the proposed algorithm scales in terms of the relevant quantities of the data and the model. The contribution of this paper is mostly experimental, leveraging fairly standard ideas from empirical Bayesian learning to introduce weight clustering effects in CNN training. This being said, it is an interesting result that such a relatively straightforward approach leads to results that are on par with state-of-the-art, but more ad-hoc, network compression techniques. The paper could be improved by clearly describing the algorithm used for training, and how it scales to large networks and datasets. Another point that would deserve further discussion is how the hyper-parameter search is performed ( not using test data I assume), and how the compared methods dealt with the search over hyper-parameters to determine the accuracy-compression tradeoff. Ideally, I think, methods should be evaluated across different points on this trade-off.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Soft Weight-Sharing for Neural Network Compression
The success of deep learning in numerous application domains created the desire to run and train them on mobile devices. This however, conflicts with their computationally, memory and energy intense nature, leading to a growing interest in compression. Recent work by Han et al. (2016) propose a pipeline that involves retraining, pruning and quantization of neural network weights, obtaining state-of-the-art compression rates. In this paper, we show that competitive compression rates can be achieved by using a version of *soft weight-sharing* (Nowlan & Hinton, 1991). Our method achieves both quantization and pruning in one simple (re-)training procedure. This point of view also exposes the relation between compression and the minimum description length (MDL) principle.
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>



This paper proposes to use an empirical Bayesian approach to learn the parameters of a neural network, and their priors. A mixture model prior over the weights leads to a clustering effect in the weight posterior distributions (which are approximated with delta peaks). This clustering effect can exploited for parameter quantisation and compression of the network parameters. The authors show that this leads to compression rates and predictive accuracy comparable to related approaches. Earlier work [Han et al. 2015] is based on a three-stage process of pruning small magnitude weights, clustering the remaining ones, and updating the cluster centres to optimise performance. The current work provides a more principled approach that does not have such an ad-hoc multi-stage structure, but a single iterative optimisation process. A first experiment, described in section 6.1 shows that an empirical Bayes’ approach, without the use of hyper priors, already leads to a pronounced clustering effect and to setting many weights to zero. In particular a compression rate of 64.2 is obtained on the LeNet300-100 model. In section 6.1 the text refers to figure C, I suppose this should be figure 1. Section 6.2 describes an experiment where hyper-priors are used, and the parameters of these distributions, as well as other hyper-parameters such as the learning rates, are being optimised using Spearmint (Snoek et al., 2012). Figure 2 shows the performance of the different points in the hyper-parameter space that have been evaluated (each trained network gives an accuracy-compressionrate point in the graph). The text claims that best results lie on a line, this seems a little opportunistic interpretation given the limited data. Moreover, it would be useful to add a small discussion on whether such a linear relationship would be expected or not. Currently the results of this experiment lack interpretation. Section 6.3 describes results obtained for both CNN models and compares results to the recent results of (Han et al., 2015) and (Guo et al., 2016). Comparable results are obtained in terms of compression rate and accuracy. The authors state that their current algorithm is too slow to be useful for larger models such as VGG-19, but they do briefly report some results obtained for this model (but do not compare to related work). It would be useful here to explain what slows the training down with respect to standard training without the weight clustering approach, and how the proposed algorithm scales in terms of the relevant quantities of the data and the model. The contribution of this paper is mostly experimental, leveraging fairly standard ideas from empirical Bayesian learning to introduce weight clustering effects in CNN training. This being said, it is an interesting result that such a relatively straightforward approach leads to results that are on par with state-of-the-art, but more ad-hoc, network compression techniques. The paper could be improved by clearly describing the algorithm used for training, and how it scales to large networks and datasets. Another point that would deserve further discussion is how the hyper-parameter search is performed ( not using test data I assume), and how the compared methods dealt with the search over hyper-parameters to determine the accuracy-compression tradeoff. Ideally, I think, methods should be evaluated across different points on this trade-off.
assistant
This paper proposes to use an empirical Bayesian approach to learn the parameters of a neural network, and their priors. A mixture model prior over the weights leads to a clustering effect in the weight posterior distributions (which are approximated with delta peaks). This clustering effect can exploited for parameter quantisation and compression of the network parameters. The authors show that this leads to compression rates and predictive accuracy comparable to related approaches. Earlier work [Han et al. 2015] is based on a three-stage process of pruning small magnitude weights, clustering the remaining ones, and updating the cluster centres to optimise performance. The current work provides a more principled approach that does not have such an ad-hoc multi-stage structure, but a single iterative optimisation process. A first experiment, described in section 6.1 shows that an empirical Bayes’ approach, without the use of hyper priors, already leads to a pronounced clustering effect and to setting many weights to zero. In particular a compression rate of 64.2 is obtained on the LeNet300-100 model. In section 6.1 the text refers to figure C, I suppose this should be figure 1. Section 6.2 describes an experiment where hyper-priors are used, and the parameters of these distributions, as well as other hyper-parameters such as the learning rates, are being optimised using Spearmint (Snoek et al., 2012). Figure 2 shows the performance of the different points in the hyper-parameter space that have been evaluated (each trained network gives an accuracy-compressionrate point in the graph). The text claims that best results lie on a line, this seems a little opportunistic interpretation given the limited data. Moreover, it would be useful to add a small discussion on whether such a linear relationship would be expected or not. Currently the results of this experiment lack interpretation. Section 6.3 describes results obtained for both CNN models and compares results to the recent results of (Han et al., 2015) and (Guo et al., 2016). Comparable results are obtained in terms of compression rate and accuracy. The authors state that their current algorithm is too slow to be useful for larger models such as VGG-19, but they do briefly report some results obtained for this model (but do not compare to related work). It would be useful here to explain what slows the training down with respect to standard training without the weight clustering approach, and how the proposed algorithm scales in terms of the relevant quantities of the data and the model. The contribution of this paper is mostly experimental, leveraging fairly standard ideas from empirical Bayesian learning to introduce weight clustering effects in CNN training. This being said, it is an interesting result that such a relatively straightforward approach leads to results that are on par with state-of-the-art, but more ad-hoc, network compression techniques. The paper could be improved by clearly describing the algorithm used for training, and how it scales to large networks and datasets. Another point that would deserve further discussion is how the hyper-parameter search is performed ( not using test data I assume), and how the compared methods dealt with the search over hyper-parameters to determine the accuracy-compression tradeoff. Ideally, I think, methods should be evaluated across different points on this trade-off.