A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks
We present a generalization bound for feedforward neural networks in terms of the product of the spectral norm of the layers and the Frobenius norm of the weights. The generalization bound is derived using a PAC-Bayes analysis.
 This paper provides a new generalization bound for feed forward networks based on a PAC-Bayesian analysis. The generalization bound depends on the spectral norm of the layers and the Frobenius norm of the weights. The resulting generalization bound is similar (though not comparable) to a recent result of Bartlett et al (2017), however the technique is different since this submission uses PAC-Bayesian analysis. The resulting proof is more simple and streamlined compared to that of Bartlett et al (2017). The paper is well presented, the result is explained and compared to other results, and the proofs seem correct. The result is not particularly different from previous ones, but the different proof technique might be a good enough reason to accept this paper. Typos: Several citations are unparenthesized when they should be. Also, after equation (6) there is a reference command that is not compiled properly.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks
We present a generalization bound for feedforward neural networks in terms of the product of the spectral norm of the layers and the Frobenius norm of the weights. The generalization bound is derived using a PAC-Bayes analysis.
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 provides a new generalization bound for feed forward networks based on a PAC-Bayesian analysis. The generalization bound depends on the spectral norm of the layers and the Frobenius norm of the weights. The resulting generalization bound is similar (though not comparable) to a recent result of Bartlett et al (2017), however the technique is different since this submission uses PAC-Bayesian analysis. The resulting proof is more simple and streamlined compared to that of Bartlett et al (2017). The paper is well presented, the result is explained and compared to other results, and the proofs seem correct. The result is not particularly different from previous ones, but the different proof technique might be a good enough reason to accept this paper. Typos: Several citations are unparenthesized when they should be. Also, after equation (6) there is a reference command that is not compiled properly.
assistant
 This paper provides a new generalization bound for feed forward networks based on a PAC-Bayesian analysis. The generalization bound depends on the spectral norm of the layers and the Frobenius norm of the weights. The resulting generalization bound is similar (though not comparable) to a recent result of Bartlett et al (2017), however the technique is different since this submission uses PAC-Bayesian analysis. The resulting proof is more simple and streamlined compared to that of Bartlett et al (2017). The paper is well presented, the result is explained and compared to other results, and the proofs seem correct. The result is not particularly different from previous ones, but the different proof technique might be a good enough reason to accept this paper. Typos: Several citations are unparenthesized when they should be. Also, after equation (6) there is a reference command that is not compiled properly.