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A study on the uncertainty of convolutional layers in deep neural networks

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arXiv 2020年

作者： Shen, Haojing Chen, Sihong Wang, Ran Big Data Institute College of Computer Science and Software Engineering Guangdong Key Lab. of Intelligent Information Processing Shenzhen University ShenzhenGuangdong518060 China College of Mathematics and Statistics Shenzhen University Shenzhen518060 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China

This paper shows a Min-Max property existing in the connection weights of the convolutional layers in a neural network structure, i.e., the LeNet. Specifically, the Min-Max property means that, during the back propagation-based training for LeNet, the weights of the convolutional layers will become far away from their centers of intervals, i.e., decreasing to their minimum or increasing to their maximum. From the perspective of uncertainty, we demonstrate that the Min-Max property corresponds to minimizing the fuzziness of the model parameters through a simplified formulation of convolution. It is experimentally confirmed that the model with the Min-Max property has a stronger adversarial robustness, thus this property can be incorporated into the design of loss function. This paper points out a changing tendency of uncertainty in the convolutional layers of LeNet structure, and gives some insights to the interpretability of convolution. © 2020, CC-BY.

关键词： Convolution

Adversarial learning with Cost-Sensitive Classes

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arXiv 2021年

作者： Shen, Haojing Chen, Sihong Wang, Ran Wang, Xizhao Big Data Institute College of Computer Science and Software Engineering Guangdong Key Lab. of Intelligent Information Processing Shenzhen University Guangdong Shenzhen518060 China The College of Mathematics and Statistics Shenzhen University Shenzhen518060 China The Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China

It is necessary to improve the performance of some special classes or to particularly protect them from attacks in adversarial learning. This paper proposes a framework combining cost-sensitive classification and adversarial learning together to train a model that can distinguish between protected and unprotected classes, such that the protected classes are less vulnerable to adversarial examples. We find in this framework an interesting phenomenon during the training of deep neural networks, called Min-Max property, that is, the absolute values of most parameters in the convolutional layer approach zero while the absolute values of a few parameters are significantly larger becoming bigger. Based on this Min-Max property which is formulated and analyzed in a view of random distribution, we further build a new defense model against adversarial examples for adversarial robustness improvement. An advantage of the built model is that it performs better than the standard one and can combine with adversarial training to achieve an improved performance. It is experimentally confirmed that, regarding the average accuracy of all classes, our model is almost as same as the existing models when an attack does not occur and is better than the existing models when an attack occurs. Specifically, regarding the accuracy of protected classes, the proposed model is much better than the existing models when an attack occurs. © 2021, CC BY.

关键词： Deep neural networks

Incorporating Hidden Layer representation into Adversarial Attacks and Defences

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arXiv 2020年

In this paper, we propose a defence strategy to improves adversarial robustness incorporating hidden layer representation. The key of this defence strategy aims to compress or filter input’s information including adversarial perturbation. And this defence strategy can be regarded as an activation function which can be applied any kind of neural networks. We also prove theoretically the effectiveness of this defense strategy under certain conditions. Besides, incorporating hidden layer representation we propose three types of adversarial attacks to generate three types of adversarial examples, respectively. The experiments show that our defence method can significantly improve the adversarial robustness of deep neural networks which achieves the state-of-the-art performance even though we do not adopt adversarial training. © 2020, CC BY.

关键词： Deep neural networks

Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation

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arXiv 2019年

作者： Gong, Huajun Wang, Changyou Zhang, Xiaotao Shenzhen Key Laboratory of Advance Machine Learning and Applications College of Mathematics and Statistics Shenzhen University Shenzhen Guangdong518060 China Department of Mathematics Purdue University West LafayetteIN47907 United States South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal University Zhong Shan Avenue West 55 Guangzhou510631 China

In this paper, inspired by the seminal work by Caffarelli-Kohn-Nirenberg [1] on the incompressible Navier-Stokes equation, we establish the existence of a suitable weak solution to the Navier-Stokes-Planck-Nernst-Poisson equation in dimension three, which is shown to be smooth away from a closed set whose 1-dimensional parabolic Hausdorff measure is zero. Copyright © 2019, The Authors. All rights reserved.

关键词： Navier Stokes equations

A Global Reweighting Approach for Cross-Domain Semantic Segmentation

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SSRN

SSRN 2022年

作者： Zhang, Yuhang Tian, Shishun Liao, Muxin Hua, Guoguang Zou, Wenbin Xu, Chen Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China Guangdong Key Laboratory of Intelligent Information Processing Shenzhen University Shenzhen518060 China Institute of Artificial Intelligence and Advanced Communication Shenzhen University Shenzhen518060 China College of Electronics and Information Engineering Shenzhen University Shenzhen518060 China College of Mathematics and Statistics Shenzhen University Shenzhen518060 China

Unsupervised domain adaptation semantic segmentation attracts much research attention due to the expensive pixel-level annotation cost. Since the adaptation difficulty of samples is different, the weight of samples should be set independently, which is called reweighting. However, existing reweighting methods only calculate local reweighting information from predicted results or context information in batch images of two domains, which may lead to over-alignment or under-alignment problems. To handle this issue, we propose a global reweighting approach. Specifically, we first define the target centroid distance, which describes the distance between the source batch data and the target centroid. Then, we introduce a Fréchet Inception Distance metric to evaluate the domain divergence and embed it into the target centroid distance. Finally, a global reweighting strategy is proposed to enhance the knowledge transferability in the source domain supervision. Extensive experiments demonstrate that our approach achieves competitive performance and helps to improve performance in other methods. © 2022, The Authors. All rights reserved.

关键词： Semantic Segmentation

GELFAND-KIRILLOV DIMENSIONS and ASSOCIATED VARIETIES of HIGHEST WEIGHT MODULES

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arXiv 2020年

作者： Bai, Zhanqiang Xiao, Wei Xie, Xun School of Mathematical Sciences Soochow University Suzhou215006 China College of Mathematics and statistics Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Guangdong Shenzhen518060 China School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China

In this paper, we present a uniform formula of Lusztig's a-functions on classical Weyl groups. Then we obtain an efficient algorithm for the Gelfand-Kirillov dimensions of simple highest weight modules of classical Lie algebras, whose highest weight is not necessarily regular or integral. To deal with type D, we prove an interesting property about domino tableaux associated with Weyl group elements by introducing an invariant, called the hollow tableau. As an application, the associated varieties of all the simple highest weight Harish-Chandra modules are explicitly determined, including the exceptional *** Codes Primary 22E47, Secondary 17B10, 20C08 Copyright © 2020, The Authors. All rights reserved.

关键词： Algebra

Simple fourier trace formulas of cubic level and applications

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arXiv 2019年

作者： Pi, Qinghua Wang, Yingnan Zhang, Lei School of Mathematics and Statistics Shandong Univeristy Weihai Weihai264209 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and Statistics Shenzhen University Shenzhen Guangdong518060 China Department of Mathematics National University of Singapore Singapore119076 Singapore

With the method of the relative trace formula and the classification of simple supercuspidal representations, we establish a simple Kuznetsov trace formula and a simple Petersson trace formula for automorphic forms on GL(2) of cubic level. As applications, we obtain some Weyl's laws for Maass newforms and a non-vanishing result for central L-values of holomorphic newforms. Copyright © 2019, The Authors. All rights reserved.

关键词：

THE BEHAVIOR OF ERROR BOUNDS VIA MOREAU ENVELOPES

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arXiv 2023年

作者： Wang, Yu Li, Shengjie Hu, Yaohua Li, Minghua Li, Xiaobing College of Mathematics and Statistics Chongqing University China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and Statistics Shenzhen University Shenzhen China The Key Laboratory of Complex Data Analysis and Artificial Intelligence of Chongqing Chongqing University of Arts and Sciences Yongchuan China College of Mathematics and Statistics Chongqing Jiaotong University China

In this paper, we first establish the equivalence of three types of error bounds: uniformized Kurdyka-Lojasiewicz (u-KL) property, uniformized level-set subdifferential error bound (u-LSEB) and uniformized Hölder error bound (u-HEB) for prox-regular functions. Then we study the behavior of the level-set subdifferential error bound (LSEB) and the local Hölder error bound (LHEB) which is expressed respectively by Moreau envelopes, under suitable assumptions. Finally, in order to illustrate our main results and to compare them with those of recent references, some examples are also given. Copyright © 2023, The Authors. All rights reserved.

关键词： Error analysis

Global small solutions to heat conductive compressible nematic liquid crystal system: Smallness on a scaling invariant quantity

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arXiv 2021年

作者： Li, Jinkai Tao, Qiang South China Research Center for Applied Mathematics and Interdisciplinary Studies School of Mathematical Sciences South China Normal University Guangzhou510631 China School of Mathematics and Statistics Shenzhen University Shenzhen518060 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China

In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established under the condition that the scaling invariant quantity (||ρ0||∞ + 1)[||ρ0||3 + (||ρ0||∞ + 1)2(||√ρ0u0||22 + ||∇d0||22)][||∇u0||22 + (||ρ0||∞ + 1)(||√ρ0E0||22 + ||∇2d0||22)] is sufficiently small with the smallness depending only on the parameters appeared in the system. Copyright © 2021, The Authors. All rights reserved.

关键词： Heat conduction