Traditional and Heavy Tailed Self Regularization in Neural Network Models
Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. Empirical and theoretical results clearly indicate that the empirical spectral density (ESD) of DNN layer matrices displays signatures of traditionally-regularized statistical models, even in the absence of exogenously specifying traditional forms of regularization, such as Dropout or Weight Norm constraints. Building on recent results in RMT, most notably its extension to Universality classes of Heavy-Tailed matrices, we develop a theory to identify 5+1 Phases of Training, corresponding to increasing amounts of Implicit Self-Regularization. For smaller and/or older DNNs, this Implicit Self-Regularization is like traditional Tikhonov regularization, in that there is a "size scale" separating signal from noise. For state-of-the-art DNNs, however, we identify a novel form of Heavy-Tailed Self-Regularization, similar to the self-organization seen in the statistical physics of disordered systems. This implicit Self-Regularization can depend strongly on the many knobs of the training process. By exploiting the generalization gap phenomena, we demonstrate that we can cause a small model to exhibit all 5+1 phases of training simply by changing the batch size.
 The paper analyzes the empirical spectral density of DNN layher matrices and compares them with the traditionally-regularized statistical models, and develop a theory to identify 5+1 phases of training based on it. The results with different batch sizes illustrate the Generalization Gap pheneomena, and explains it as being causes by implicit self-regularization. However, the paper seems a little bit handwavy to me, without any serious theoretical justification. For example, why are .mu=2 and 4 chosen as the threshold between weakly/moderately/very heavy-tailed? In addition, the paper is build upon o the 5+1 model as in Figure 2 and the graphical comparison between the empirical ESD and the expected ESD of the five models in Table 1, and they lack any mathematical/rigorous definition---see table 2. The simulations are performs over a particular data set and a particular setting, and I wonder if the observations would be different for a different data set and a different setting. As a result, it may give some important intuition, but the content is not sufficiently rigorous to my knowledge.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Traditional and Heavy Tailed Self Regularization in Neural Network Models
Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. Empirical and theoretical results clearly indicate that the empirical spectral density (ESD) of DNN layer matrices displays signatures of traditionally-regularized statistical models, even in the absence of exogenously specifying traditional forms of regularization, such as Dropout or Weight Norm constraints. Building on recent results in RMT, most notably its extension to Universality classes of Heavy-Tailed matrices, we develop a theory to identify 5+1 Phases of Training, corresponding to increasing amounts of Implicit Self-Regularization. For smaller and/or older DNNs, this Implicit Self-Regularization is like traditional Tikhonov regularization, in that there is a "size scale" separating signal from noise. For state-of-the-art DNNs, however, we identify a novel form of Heavy-Tailed Self-Regularization, similar to the self-organization seen in the statistical physics of disordered systems. This implicit Self-Regularization can depend strongly on the many knobs of the training process. By exploiting the generalization gap phenomena, we demonstrate that we can cause a small model to exhibit all 5+1 phases of training simply by changing the batch size.
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 paper analyzes the empirical spectral density of DNN layher matrices and compares them with the traditionally-regularized statistical models, and develop a theory to identify 5+1 phases of training based on it. The results with different batch sizes illustrate the Generalization Gap pheneomena, and explains it as being causes by implicit self-regularization. However, the paper seems a little bit handwavy to me, without any serious theoretical justification. For example, why are .mu=2 and 4 chosen as the threshold between weakly/moderately/very heavy-tailed? In addition, the paper is build upon o the 5+1 model as in Figure 2 and the graphical comparison between the empirical ESD and the expected ESD of the five models in Table 1, and they lack any mathematical/rigorous definition---see table 2. The simulations are performs over a particular data set and a particular setting, and I wonder if the observations would be different for a different data set and a different setting. As a result, it may give some important intuition, but the content is not sufficiently rigorous to my knowledge.
assistant
 The paper analyzes the empirical spectral density of DNN layher matrices and compares them with the traditionally-regularized statistical models, and develop a theory to identify 5+1 phases of training based on it. The results with different batch sizes illustrate the Generalization Gap pheneomena, and explains it as being causes by implicit self-regularization. However, the paper seems a little bit handwavy to me, without any serious theoretical justification. For example, why are .mu=2 and 4 chosen as the threshold between weakly/moderately/very heavy-tailed? In addition, the paper is build upon o the 5+1 model as in Figure 2 and the graphical comparison between the empirical ESD and the expected ESD of the five models in Table 1, and they lack any mathematical/rigorous definition---see table 2. The simulations are performs over a particular data set and a particular setting, and I wonder if the observations would be different for a different data set and a different setting. As a result, it may give some important intuition, but the content is not sufficiently rigorous to my knowledge.