A comparison of second-order methods for deep convolutional neural networks
Despite many second-order methods have been proposed to train neural networks, most of the results were done on smaller single layer fully connected networks, so we still cannot conclude whether it*s useful in training deep convolutional networks. In this study, we conduct extensive experiments to answer the question "whether second-order method is useful for deep learning?". In our analysis, we find out although currently second-order methods are too slow to be applied in practice, it can reduce training loss in fewer number of iterations compared with SGD. In addition, we have the following interesting findings: (1) When using a large batch size, inexact-Newton methods will converge much faster than SGD. Therefore inexact-Newton method could be a better choice in distributed training of deep networks. (2) Quasi-newton methods are competitive with SGD even when using ReLu activation function (which has no curvature) on residual networks. However, current methods are too sensitive to parameters and not easy to tune for different settings. Therefore, quasi-newton methods with more self-adjusting mechanisms might be more useful than SGD in training deeper networks.
 This paper presents a comparative study on second-order optimization methods for CNNs. Overall, the topic is interesting and would be useful for the community. However, I think there are important issues about the paper: 1) The paper is not very well-written. The language is sometimes very informal, there are many grammatical mistakes and typos. The paper should be carefully proofread. 2) For such a comparative study, the number of algorithms and the number of datasets are quite little. The authors do not mention several important methods such as (not exhaustive) Schraudolph, N. N., Yu, J., and Günter, S. A stochastic quasi-Newton method for online convex optimization. Gurbuzbalaban et al, A globally convergent incremental Newton method (and other papers of the same authors) A Linearly-Convergent Stochastic L-BFGS Algorithm, Moritz et al 3) The experiment details are not provided. It is not clear what parameters are used and how. 4) There are some vague statements such as "this scheme does not work" or "fixed learning rates are not applicable". For instance, for the latter I cannot see a reason and the paper does not provide any convincing results. Even though the paper attempts to address an important point in deep learning, I do not believe that the presented results form evidence for such rather bold statements.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
A comparison of second-order methods for deep convolutional neural networks
Despite many second-order methods have been proposed to train neural networks, most of the results were done on smaller single layer fully connected networks, so we still cannot conclude whether it*s useful in training deep convolutional networks. In this study, we conduct extensive experiments to answer the question "whether second-order method is useful for deep learning?". In our analysis, we find out although currently second-order methods are too slow to be applied in practice, it can reduce training loss in fewer number of iterations compared with SGD. In addition, we have the following interesting findings: (1) When using a large batch size, inexact-Newton methods will converge much faster than SGD. Therefore inexact-Newton method could be a better choice in distributed training of deep networks. (2) Quasi-newton methods are competitive with SGD even when using ReLu activation function (which has no curvature) on residual networks. However, current methods are too sensitive to parameters and not easy to tune for different settings. Therefore, quasi-newton methods with more self-adjusting mechanisms might be more useful than SGD in training deeper networks.
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 comparative study on second-order optimization methods for CNNs. Overall, the topic is interesting and would be useful for the community. However, I think there are important issues about the paper: 1) The paper is not very well-written. The language is sometimes very informal, there are many grammatical mistakes and typos. The paper should be carefully proofread. 2) For such a comparative study, the number of algorithms and the number of datasets are quite little. The authors do not mention several important methods such as (not exhaustive) Schraudolph, N. N., Yu, J., and Günter, S. A stochastic quasi-Newton method for online convex optimization. Gurbuzbalaban et al, A globally convergent incremental Newton method (and other papers of the same authors) A Linearly-Convergent Stochastic L-BFGS Algorithm, Moritz et al 3) The experiment details are not provided. It is not clear what parameters are used and how. 4) There are some vague statements such as "this scheme does not work" or "fixed learning rates are not applicable". For instance, for the latter I cannot see a reason and the paper does not provide any convincing results. Even though the paper attempts to address an important point in deep learning, I do not believe that the presented results form evidence for such rather bold statements.
assistant
 This paper presents a comparative study on second-order optimization methods for CNNs. Overall, the topic is interesting and would be useful for the community. However, I think there are important issues about the paper: 1) The paper is not very well-written. The language is sometimes very informal, there are many grammatical mistakes and typos. The paper should be carefully proofread. 2) For such a comparative study, the number of algorithms and the number of datasets are quite little. The authors do not mention several important methods such as (not exhaustive) Schraudolph, N. N., Yu, J., and Günter, S. A stochastic quasi-Newton method for online convex optimization. Gurbuzbalaban et al, A globally convergent incremental Newton method (and other papers of the same authors) A Linearly-Convergent Stochastic L-BFGS Algorithm, Moritz et al 3) The experiment details are not provided. It is not clear what parameters are used and how. 4) There are some vague statements such as "this scheme does not work" or "fixed learning rates are not applicable". For instance, for the latter I cannot see a reason and the paper does not provide any convincing results. Even though the paper attempts to address an important point in deep learning, I do not believe that the presented results form evidence for such rather bold statements.