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.
This paper studies an interesting phenomenon in neural network models that the classifier*s prediction at a one input will not be significantly perturbed after the classifier is updated via sgd at another input that is dissimilar from the former one. This phenomenon is termed as the local elasticity, which provides another perspective seeking to interpret the neural networks. They present that this local elasticity characteristic does not hold for linear models. To further investigate this property, the paper introduces the relative similarity and kernelized similarity based on which a k-means like clustering algorithm is developed to further find fine-grained clusters within a coarse-grained category, like dogs and cats from the mammal category. Interpreting neural networks is a hot research topic, and a paper advancing knowledge in this area is certainly welcome. The paper is well presented (with a small typo in the definition of S_ker(x,x)). In the experiments, it will be interesting to further investigate how the local elastic property changes with large batch size in that large batch size may encourage more diversity of the examples in a batch. Furthermore, it will be even more interesting to explore how these similarities can improve the performance of a simple k-nearest neighbor classifier.
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>



This paper studies an interesting phenomenon in neural network models that the classifier*s prediction at a one input will not be significantly perturbed after the classifier is updated via sgd at another input that is dissimilar from the former one. This phenomenon is termed as the local elasticity, which provides another perspective seeking to interpret the neural networks. They present that this local elasticity characteristic does not hold for linear models. To further investigate this property, the paper introduces the relative similarity and kernelized similarity based on which a k-means like clustering algorithm is developed to further find fine-grained clusters within a coarse-grained category, like dogs and cats from the mammal category. Interpreting neural networks is a hot research topic, and a paper advancing knowledge in this area is certainly welcome. The paper is well presented (with a small typo in the definition of S_ker(x,x)). In the experiments, it will be interesting to further investigate how the local elastic property changes with large batch size in that large batch size may encourage more diversity of the examples in a batch. Furthermore, it will be even more interesting to explore how these similarities can improve the performance of a simple k-nearest neighbor classifier.
assistant
This paper studies an interesting phenomenon in neural network models that the classifier*s prediction at a one input will not be significantly perturbed after the classifier is updated via sgd at another input that is dissimilar from the former one. This phenomenon is termed as the local elasticity, which provides another perspective seeking to interpret the neural networks. They present that this local elasticity characteristic does not hold for linear models. To further investigate this property, the paper introduces the relative similarity and kernelized similarity based on which a k-means like clustering algorithm is developed to further find fine-grained clusters within a coarse-grained category, like dogs and cats from the mammal category. Interpreting neural networks is a hot research topic, and a paper advancing knowledge in this area is certainly welcome. The paper is well presented (with a small typo in the definition of S_ker(x,x)). In the experiments, it will be interesting to further investigate how the local elastic property changes with large batch size in that large batch size may encourage more diversity of the examples in a batch. Furthermore, it will be even more interesting to explore how these similarities can improve the performance of a simple k-nearest neighbor classifier.