REPRESENTATION COMPRESSION AND GENERALIZATION IN DEEP NEURAL NETWORKS
Understanding the groundbreaking performance of Deep Neural Networks is one of the greatest challenges to the scientific community today. In this work, we introduce an information theoretic viewpoint on the behavior of deep networks optimization processes and their generalization abilities. By studying the Information Plane, the plane of the mutual information between the input variable and the desired label, for each hidden layer. Specifically, we show that the training of the network is characterized by a rapid increase in the mutual information (MI) between the layers and the target label, followed by a longer decrease in the MI between the layers and the input variable. Further, we explicitly show that these two fundamental information-theoretic quantities correspond to the generalization error of the network, as a result of introducing a new generalization bound that is exponential in the representation compression. The analysis focuses on typical patterns of large-scale problems. For this purpose, we introduce a novel analytic bound on the mutual information between consecutive layers in the network. An important consequence of our analysis is a super-linear boost in training time with the number of non-degenerate hidden layers, demonstrating the computational benefit of the hidden layers.
 The authors are providing an information theoretic viewpoint on the behavior of DNN based on the information bottleneck. The clarity of the paper is my main concern. It contains quite a number of typos and errors. For example, in section 6, the results of MNIST in the first experiment was presented after introducing the second experiment. Also, the results shown in Fig 1b seems to have nothing to do with Fig. 1a. It makes use of some existing results from other literature but it is not clearly explained how and why the results are being used. It might be a very good paper if the writing could be improved. The paper also contains some experimental results. But they are too brief and I do not consider the experiments as sufficient to justify the correctness of the bounds proved in the paper.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
REPRESENTATION COMPRESSION AND GENERALIZATION IN DEEP NEURAL NETWORKS
Understanding the groundbreaking performance of Deep Neural Networks is one of the greatest challenges to the scientific community today. In this work, we introduce an information theoretic viewpoint on the behavior of deep networks optimization processes and their generalization abilities. By studying the Information Plane, the plane of the mutual information between the input variable and the desired label, for each hidden layer. Specifically, we show that the training of the network is characterized by a rapid increase in the mutual information (MI) between the layers and the target label, followed by a longer decrease in the MI between the layers and the input variable. Further, we explicitly show that these two fundamental information-theoretic quantities correspond to the generalization error of the network, as a result of introducing a new generalization bound that is exponential in the representation compression. The analysis focuses on typical patterns of large-scale problems. For this purpose, we introduce a novel analytic bound on the mutual information between consecutive layers in the network. An important consequence of our analysis is a super-linear boost in training time with the number of non-degenerate hidden layers, demonstrating the computational benefit of the hidden layers.
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 are providing an information theoretic viewpoint on the behavior of DNN based on the information bottleneck. The clarity of the paper is my main concern. It contains quite a number of typos and errors. For example, in section 6, the results of MNIST in the first experiment was presented after introducing the second experiment. Also, the results shown in Fig 1b seems to have nothing to do with Fig. 1a. It makes use of some existing results from other literature but it is not clearly explained how and why the results are being used. It might be a very good paper if the writing could be improved. The paper also contains some experimental results. But they are too brief and I do not consider the experiments as sufficient to justify the correctness of the bounds proved in the paper.
assistant
 The authors are providing an information theoretic viewpoint on the behavior of DNN based on the information bottleneck. The clarity of the paper is my main concern. It contains quite a number of typos and errors. For example, in section 6, the results of MNIST in the first experiment was presented after introducing the second experiment. Also, the results shown in Fig 1b seems to have nothing to do with Fig. 1a. It makes use of some existing results from other literature but it is not clearly explained how and why the results are being used. It might be a very good paper if the writing could be improved. The paper also contains some experimental results. But they are too brief and I do not consider the experiments as sufficient to justify the correctness of the bounds proved in the paper.