Learning Sparse Neural Networks through L_0 Regularization
We propose a practical method for norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of regularization. However, since the norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected regularized objective is differentiable with respect to the distribution parameters. We further propose the emph{hard concrete} distribution for the gates, which is obtained by ``stretching** a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer.
 This paper presents a continuous surrogate for the ell_0 norm and focuses on its applications in regularized empirical regularized minimization. The proposed continuous relaxation scheme allows for gradient based-stochastic optimization for binary discrete variables under the reparameterization trick, and extends the original binary concrete distribution by allowing the parameter taking values of exact zeros and ones, with additional stretching and thresholding operations. Under a compound construction of sparsity, the proposed approach can easily incorporate group sparsity by sharing supports among the grouped variables, or be combined with other types of regularizations on the magnitude of non-zero components. The efficacy of the proposed method in sparsification and speedup is demonstrated in two experiments with comparisons against a few baseline methods. Pros: - The paper is clearly written, self-contained and a pleasure to read. - Based on the evidence provided, the procedure seems to be a useful continuous relaxation scheme to consider in handling optimization with spike and slab regularization Cons: - It would be interesting to see how the induced penalty behaves in terms shrinkage comparing against ell_0 and other ell_p choices - It is unclear what properties does the proposed hard-concrete distribution have, e.g., closed-form density, convexity, etc. - If the authors can offer a rigorous analysis on the influence of base concrete distribution and provide more guidance on how to choose the stretching parameters in practice, this paper would be more significant
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Sparse Neural Networks through L_0 Regularization
We propose a practical method for norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of regularization. However, since the norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected regularized objective is differentiable with respect to the distribution parameters. We further propose the emph{hard concrete} distribution for the gates, which is obtained by ``stretching** a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer.
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 presents a continuous surrogate for the ell_0 norm and focuses on its applications in regularized empirical regularized minimization. The proposed continuous relaxation scheme allows for gradient based-stochastic optimization for binary discrete variables under the reparameterization trick, and extends the original binary concrete distribution by allowing the parameter taking values of exact zeros and ones, with additional stretching and thresholding operations. Under a compound construction of sparsity, the proposed approach can easily incorporate group sparsity by sharing supports among the grouped variables, or be combined with other types of regularizations on the magnitude of non-zero components. The efficacy of the proposed method in sparsification and speedup is demonstrated in two experiments with comparisons against a few baseline methods. Pros: - The paper is clearly written, self-contained and a pleasure to read. - Based on the evidence provided, the procedure seems to be a useful continuous relaxation scheme to consider in handling optimization with spike and slab regularization Cons: - It would be interesting to see how the induced penalty behaves in terms shrinkage comparing against ell_0 and other ell_p choices - It is unclear what properties does the proposed hard-concrete distribution have, e.g., closed-form density, convexity, etc. - If the authors can offer a rigorous analysis on the influence of base concrete distribution and provide more guidance on how to choose the stretching parameters in practice, this paper would be more significant
assistant
 This paper presents a continuous surrogate for the ell_0 norm and focuses on its applications in regularized empirical regularized minimization. The proposed continuous relaxation scheme allows for gradient based-stochastic optimization for binary discrete variables under the reparameterization trick, and extends the original binary concrete distribution by allowing the parameter taking values of exact zeros and ones, with additional stretching and thresholding operations. Under a compound construction of sparsity, the proposed approach can easily incorporate group sparsity by sharing supports among the grouped variables, or be combined with other types of regularizations on the magnitude of non-zero components. The efficacy of the proposed method in sparsification and speedup is demonstrated in two experiments with comparisons against a few baseline methods. Pros: - The paper is clearly written, self-contained and a pleasure to read. - Based on the evidence provided, the procedure seems to be a useful continuous relaxation scheme to consider in handling optimization with spike and slab regularization Cons: - It would be interesting to see how the induced penalty behaves in terms shrinkage comparing against ell_0 and other ell_p choices - It is unclear what properties does the proposed hard-concrete distribution have, e.g., closed-form density, convexity, etc. - If the authors can offer a rigorous analysis on the influence of base concrete distribution and provide more guidance on how to choose the stretching parameters in practice, this paper would be more significant