The Local Elasticity of Neural Networks
This paper presents a phenomenon in neural networks that we refer to as local elasticity. Roughly speaking, a classifier is said to be locally elastic if its prediction at a feature vector x* is not significantly perturbed, after the classifier is updated via stochastic gradient descent at a (labeled) feature vector x that is dissimilar to x* in a certain sense. This phenomenon is shown to persist for neural networks with nonlinear activation functions through extensive simulations on synthetic datasets, whereas this is not the case for linear classifiers. In addition, we offer a geometric interpretation of local elasticity using the neural tangent kernel (Jacot et al., 2018). Building on top of local elasticity, we obtain pairwise similarity measures between feature vectors, which can be used for clustering in conjunction with K-means. The effectiveness of the clustering algorithm on the MNIST and CIFAR-10 datasets in turn confirms the hypothesis of local elasticity of neural networks on real-life data. Finally, we discuss implications of local elasticity to shed light on several intriguing aspects of deep neural networks.
The paper contributes to the understanding of neural networks and provides a new clustering technique: 1) The paper introduces the interesting notion of local elasticity which considers the relative variation in output values for two different inputs before and after an SGD-style update; 2) The derived similarity metric between input samples (obtained by as SGD unfolds) can be used for clustering and is amenable to a kernelized formulation; 3) Empirical measurements on visual classification tasks show that the new similarity metric can offer a better clustering performance than PCA + K-means. I found the paper very interesting but the writing appeared somewhat unclear at times. I believe that some rewriting is needed for the authors to argue that the newly introduced elasticity metric provides a significantly new understanding of neural networks. In particular, I did not find the argumentation around explaining generalization to be very convincing or clear. The kernelized formulation of the elasticity metric seems compelling and I found that turning the insights developed by the theoretical section of the paper into an actionable algorithm for clustering was a nice contribution. Unfortunately, the empirical results did not really convince me that the resulting clustering algorithm really improves on the SOTA in clustering as only relatively weak baselines were considered. I believe that considering more solid baselines for the clustering experiments would help.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
The Local Elasticity of Neural Networks
This paper presents a phenomenon in neural networks that we refer to as local elasticity. Roughly speaking, a classifier is said to be locally elastic if its prediction at a feature vector x* is not significantly perturbed, after the classifier is updated via stochastic gradient descent at a (labeled) feature vector x that is dissimilar to x* in a certain sense. This phenomenon is shown to persist for neural networks with nonlinear activation functions through extensive simulations on synthetic datasets, whereas this is not the case for linear classifiers. In addition, we offer a geometric interpretation of local elasticity using the neural tangent kernel (Jacot et al., 2018). Building on top of local elasticity, we obtain pairwise similarity measures between feature vectors, which can be used for clustering in conjunction with K-means. The effectiveness of the clustering algorithm on the MNIST and CIFAR-10 datasets in turn confirms the hypothesis of local elasticity of neural networks on real-life data. Finally, we discuss implications of local elasticity to shed light on several intriguing aspects of deep neural 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>



The paper contributes to the understanding of neural networks and provides a new clustering technique: 1) The paper introduces the interesting notion of local elasticity which considers the relative variation in output values for two different inputs before and after an SGD-style update; 2) The derived similarity metric between input samples (obtained by as SGD unfolds) can be used for clustering and is amenable to a kernelized formulation; 3) Empirical measurements on visual classification tasks show that the new similarity metric can offer a better clustering performance than PCA + K-means. I found the paper very interesting but the writing appeared somewhat unclear at times. I believe that some rewriting is needed for the authors to argue that the newly introduced elasticity metric provides a significantly new understanding of neural networks. In particular, I did not find the argumentation around explaining generalization to be very convincing or clear. The kernelized formulation of the elasticity metric seems compelling and I found that turning the insights developed by the theoretical section of the paper into an actionable algorithm for clustering was a nice contribution. Unfortunately, the empirical results did not really convince me that the resulting clustering algorithm really improves on the SOTA in clustering as only relatively weak baselines were considered. I believe that considering more solid baselines for the clustering experiments would help.
assistant
The paper contributes to the understanding of neural networks and provides a new clustering technique: 1) The paper introduces the interesting notion of local elasticity which considers the relative variation in output values for two different inputs before and after an SGD-style update; 2) The derived similarity metric between input samples (obtained by as SGD unfolds) can be used for clustering and is amenable to a kernelized formulation; 3) Empirical measurements on visual classification tasks show that the new similarity metric can offer a better clustering performance than PCA + K-means. I found the paper very interesting but the writing appeared somewhat unclear at times. I believe that some rewriting is needed for the authors to argue that the newly introduced elasticity metric provides a significantly new understanding of neural networks. In particular, I did not find the argumentation around explaining generalization to be very convincing or clear. The kernelized formulation of the elasticity metric seems compelling and I found that turning the insights developed by the theoretical section of the paper into an actionable algorithm for clustering was a nice contribution. Unfortunately, the empirical results did not really convince me that the resulting clustering algorithm really improves on the SOTA in clustering as only relatively weak baselines were considered. I believe that considering more solid baselines for the clustering experiments would help.