The Blessing of Dimensionality: An Empirical Study of Generalization
The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are still quite loose, and analysis does not always lead to true understanding. The goal of this work is to make generalization more intuitive. Using visualization methods, we discuss the mystery of generalization, the geometry of loss landscapes, and how the curse (or, rather, the blessing) of dimensionality causes optimizers to settle into minima that generalize well.
In this paper the authors aim to develop an intuition for why neural networks (NNs) generalize so well, despite often being overparametrized for the given problem. The paper is well written exploring a very interesting issue. It provides a good discussion of why generalization is puzzling, related work on the attempts to improve generalization bounds for NNs, and qualitative discussion of possibly answers to this problem. Despite this, we feel that a much more experimentation should be done to address some of the hypothesis in the paper. Also, it would have been helpful, if some of the results and figures were presented much earlier in the paper. What follows are the pros and cons / discussion points / styling suggestions the authors could choose to address: [pros] - Well-written - A good survey of related literature and concepts - Interesting visualizations [cons / points / styling] - The placement of Figure 1 seems arbitrary as you refer to it for the first time on Page 3. This would not be such a big problem; however, it divides the paragraph in two without need to. Could you perhaps place the figure and caption on the bottom of the page? - Is there a reference for “implicit regularization”? - On page 4, it would have been helpful to provide examples of “linking the intuitive arguments back to theory” - It would be helpful to provide more details on the filter-normalization scheme. - On page 4, could you explain what you mean by “wide margin classification is replaced with an implicit regulation (regularization - ?) that promotes the closely related notion of ‘flatness’ “. How is “flatness” encouraged as a prior? Through the choice of an appropriate loss function? Would it be perhaps more suited for a longer format, e.g. Journal of Machine Leaning Research?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
The Blessing of Dimensionality: An Empirical Study of Generalization
The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are still quite loose, and analysis does not always lead to true understanding. The goal of this work is to make generalization more intuitive. Using visualization methods, we discuss the mystery of generalization, the geometry of loss landscapes, and how the curse (or, rather, the blessing) of dimensionality causes optimizers to settle into minima that generalize well.
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>



In this paper the authors aim to develop an intuition for why neural networks (NNs) generalize so well, despite often being overparametrized for the given problem. The paper is well written exploring a very interesting issue. It provides a good discussion of why generalization is puzzling, related work on the attempts to improve generalization bounds for NNs, and qualitative discussion of possibly answers to this problem. Despite this, we feel that a much more experimentation should be done to address some of the hypothesis in the paper. Also, it would have been helpful, if some of the results and figures were presented much earlier in the paper. What follows are the pros and cons / discussion points / styling suggestions the authors could choose to address: [pros] - Well-written - A good survey of related literature and concepts - Interesting visualizations [cons / points / styling] - The placement of Figure 1 seems arbitrary as you refer to it for the first time on Page 3. This would not be such a big problem; however, it divides the paragraph in two without need to. Could you perhaps place the figure and caption on the bottom of the page? - Is there a reference for “implicit regularization”? - On page 4, it would have been helpful to provide examples of “linking the intuitive arguments back to theory” - It would be helpful to provide more details on the filter-normalization scheme. - On page 4, could you explain what you mean by “wide margin classification is replaced with an implicit regulation (regularization - ?) that promotes the closely related notion of ‘flatness’ “. How is “flatness” encouraged as a prior? Through the choice of an appropriate loss function? Would it be perhaps more suited for a longer format, e.g. Journal of Machine Leaning Research?
assistant
In this paper the authors aim to develop an intuition for why neural networks (NNs) generalize so well, despite often being overparametrized for the given problem. The paper is well written exploring a very interesting issue. It provides a good discussion of why generalization is puzzling, related work on the attempts to improve generalization bounds for NNs, and qualitative discussion of possibly answers to this problem. Despite this, we feel that a much more experimentation should be done to address some of the hypothesis in the paper. Also, it would have been helpful, if some of the results and figures were presented much earlier in the paper. What follows are the pros and cons / discussion points / styling suggestions the authors could choose to address: [pros] - Well-written - A good survey of related literature and concepts - Interesting visualizations [cons / points / styling] - The placement of Figure 1 seems arbitrary as you refer to it for the first time on Page 3. This would not be such a big problem; however, it divides the paragraph in two without need to. Could you perhaps place the figure and caption on the bottom of the page? - Is there a reference for “implicit regularization”? - On page 4, it would have been helpful to provide examples of “linking the intuitive arguments back to theory” - It would be helpful to provide more details on the filter-normalization scheme. - On page 4, could you explain what you mean by “wide margin classification is replaced with an implicit regulation (regularization - ?) that promotes the closely related notion of ‘flatness’ “. How is “flatness” encouraged as a prior? Through the choice of an appropriate loss function? Would it be perhaps more suited for a longer format, e.g. Journal of Machine Leaning Research?