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Neural Processing Letters

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03-01-2021

Computation of CNN’s Sensitivity to Input Perturbation

Authors: Lin Xiang, Xiaoqin Zeng, Shengli Wu, Yanjun Liu, Baohua Yuan

Published in: Neural Processing Letters | Issue 1/2021

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Abstract

Although Convolutional Neural Networks (CNNs) are considered as being "approximately invariant" to nuisance perturbations such as image transformation, shift, scaling, and other small deformations, some existing studies show that intense noises can cause noticeable variation to CNNs’ outputs. This paper focuses on exploring a method of measuring sensitivity by observing corresponding output variation to input perturbation on CNNs. The sensitivity is statistically defined in a bottom-up way from neuron to layer, and finally to the entire CNN network. An iterative algorithm is proposed for approximating the defined sensitivity. On the basic architecture of CNNs, the theoretically computed sensitivity is verified on the MNIST database with four types of commonly used noise distributions: Gaussian, Uniform, Salt and Pepper, and Rayleigh. Experimental results show the theoretical sensitivity is on the one hand in agreement with the actual output variation what on the maps, layers or entire networks are, and on the other hand an applicable quantitative measure for robust network selection.

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Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In: Advances in neural information processing systems, pp 1097–1105

Simon M, Rodner E (2015) Neural activation constellations: unsupervised part model discovery with convolutional networks. In: Proceedings of the IEEE international conference on computer vision, pp 1143–1151

Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. ArXiv preprint. http://arxiv.org/abs/1409.1556

Karpathy A et al (2014) Large-scale video classification with convolutional neural networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 1725–1732

Girshick R et al (2014) Rich feature hierarchies for accurate object detection and semantic segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 580–587

Kalchbrenner N, Grefenstette E, Blunsom P (2014) A convolutional neural network for modeling sentences. arXiv preprint http://arxiv.org/abs/1404.2188

Zhang Y, Wallace B (2015) A sensitivity analysis of (and practitioners' guide to) convolutional neural networks for sentence classification. arXiv preprint http://arxiv.org/abs/1510.03820

Brust CA et al (2015) Convolutional patch networks with spatial prior for road detection and urban scene understanding. arXiv preprint http://arxiv.org/abs/1502.06344

Hariharan B et al (2015) Hypercolumns for object segmentation and fine-grained localization. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 447–456

10.

Fukushima K, Miyake S (1982) Neocognitron: a self-organizing neural network model for a mechanism of visual pattern recognition, Competition and cooperation in neural nets. Springer, Berlin , pp 267–285

11.

Zeiler MD, Fergus R (2014) Visualizing and understanding convolutional networks. In: European conference on computer vision, pp 818–833

12.

Rodner E et al (2016) Fine-grained recognition in the noisy wild: Sensitivity analysis of convolutional neural networks approaches. arXiv preprint http://arxiv.org/abs/1610.06756

13.

Kwon S et al (2016). Measuring error-tolerance in SRAM architecture on hardware accelerated neural network. In: 2016 IEEE international conference on consumer electronics-Asia, pp 1–4

14.

Szegedy C et al (2013) Intriguing properties of neural networks. arXiv preprint http://arxiv.org/abs/1312.6199

15.

Fawzi A, Fawzi O, Frossard P (2018) Analysis of classifiers’ robustness to adversarial perturbations. Mach Learn 107(3):481–508MathSciNetCrossRef

16.

Fawzi A et al (2016) Robustness of classifiers: from adversarial to random noise. In: Advances in neural information processing systems, pp 1632–1640

17.

Moosavi D, Seyed M (2017) Universal adversarial perturbations. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 86–94

18.

Sharif M et al (2016) Accessorize to a crime: real and stealthy attacks on state-of-the-art face recognition. In: Proceedings of the 2016 ACM SIGSAC conference on computer and communications security, pp 1528–1540

19.

Akhtar N, Mian A (2018) Threat of adversarial attacks on deep learning in computer vision: a survey. arXiv preprint http://arxiv.org/abs/1801.00553

20.

Novak R el al (2018) Sensitivity and generalization in neural networks: an empirical study. In: International conference on learning representations. arXiv preprint http://arxiv.org/abs/1802.08760.

21.

Moosavi D el al (2016) Deepfool: a simple and accurate method to fool deep neural networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 2574–2582

22.

Hein M, Andriushchenko M (2017) Formal guarantees on the robustness of a classifier against adversarial manipulation. In: Advances in neural information processing systems, pp 2266–2276

23.

Zhang J, Huang C (2020) Dynamics analysis on a class of delayed neural networks involving inertial terms. Adv Differ Equ 2020:120. https://doi.org/10.1186/s13662-020-02566-4MathSciNetCrossRef

24.

Yang X et al (2019) Dynamic properties of foreign exchange complex network. Mathematics 7:832CrossRef

25.

Huang C, Tan Y (2020) Global behavior of a reaction–diffusion model with time delay and Dirichlet condition. J Differ Equ 271:186–215MathSciNetCrossRef

26.

Fawzi A et al (2017) The robustness of deep networks: a geometrical perspective. IEEE Signal Process Mag 34(6):50–62CrossRef

27.

Saltelli A (2002) Sensitivity analysis for importance assessment. Risk Anal 22(3):579–590CrossRef

28.

Saltelli A et al (2019) Why so many published sensitivity analyses are false: a systematic review of sensitivity analysis practices. Environ Model Softw 114:29–39CrossRef

29.

Saltelli A et al (2008) Global sensitivity analysis: the primer. Wiley, ChichesterMATH

30.

Veiga D et al (2015) Global sensitivity analysis with dependence measures. J Stat Comput Simul 85(7):1283–1305MathSciNetCrossRef

31.

Stevenson M, Winter R, Widrow B (1990) Sensitivity of feedforward neural networks to weight errors. IEEE Trans Neural Netw 1(1):71–80CrossRef

32.

Piche SW et al (1995) The selection of weight accuracies for Madalines. IEEE Trans Neural Netw 6(2):432–445CrossRef

33.

Zeng X, Wang Y, Zhang K (2006) Computation of Adalines’ sensitivity to weight perturbation. IEEE Trans Neural Netw 17(2):515–519CrossRef

34.

Wang Y et al (2006) Computation of Madalines’ sensitivity to input and weight perturbations. Neural Comput 18(11):2854–2877MathSciNetCrossRef

35.

Choi JY, Choi CH (1992) Sensitivity analysis of multilayer perceptron with differentiable activation functions. IEEE Trans Neural Netw 3(1):101–107CrossRef

36.

Fu L, Chen T (1993) Sensitivity analysis for input vector in multilayer feedforward neural networks. In: IEEE international conference on neural networks, pp 215–218

37.

Yeung D, Sun X (2002) Using function approximation to analyze the sensitivity of MLP with antisymmetric squashing activation function. IEEE Trans Neural Netw 13(1):34–44CrossRef

38.

Yang S, Ho C, Siu S (2007) Sensitivity analysis of the split-complex valued multilayer perceptron due to the errors of the iid inputs and weights. IEEE Trans Neural Netw 18(5):1280–1293CrossRef

39.

Zeng X, Yeung D (2001) Sensitivity analysis of multilayer perceptron to input and weight perturbations. IEEE Trans Neural Netw 12(6):1358–1366CrossRef

40.

Zeng X, Yeung D (2003) A quantified sensitivity measure for multilayer perceptron to input perturbation. Neural Comput 15(1):183–212CrossRef

41.

Ng WWY et al (2002) Statistical output sensitivity to input and weight perturbations of radial basis function neural networks. IEEE Int Conf Syst Man Cybern 2:503–508CrossRef

42.

Cheng A, Yeung D (1999) Sensitivity analysis of neocognitron. IEEE Trans Syst Man Cybern C Appl Rev 29(2):238–249CrossRef

43.

Chen D et al (2020) Fixed time synchronization of delayed quaternion-valued memristor-based neural Networks. Adv Differ Equ 2020:92. https://doi.org/10.1186/s13662-020-02560-wMathSciNetCrossRef

44.

Cao JD et al (2020) Zagreb connection indices of molecular graphs based on operations. Complexity 2020:1–15

45.

Zhou Y et al (2020) Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control. Appl Math Comput 376:125157MathSciNetMATH

46.

Yeung D et al (2010) Sensitivity analysis for neural networks. Springer, BerlinCrossRef

47.

Wang W et al (2020) Bipartite formation problem of second-order nonlinear multi-agent systems with hybrid impulses. Appl Math Comput 370:124926MathSciNetMATH

48.

Huang C et al (2020) Asymptotic behavior for a class of population dynamics. Mathematics 5(4):3378–3390MathSciNet

49.

Kumari S et al (2020) On the construction, properties and Hausdorff dimension of random cantor one pth set. Mathematics 5(4):3138–3155MathSciNet

50.

Zhang Y, Wallace B (2017) Sensitivity analysis of (and practitioners’ guide to) convolutional neural networks for sentence classification. In: International joint conference on natural language processing, pp 253–263

51.

Rawat W, Wang Z (2017) Deep convolutional neural networks for image classification: a comprehensive review. Neural Comput 29(9):2352–2449MathSciNetCrossRef

52.

Shu H, Zhu H (2019) Sensitivity analysis of deep neural networks. Proc AAAI Conf Artif Intell 33:4943–4950

Title: Computation of CNN’s Sensitivity to Input Perturbation
Authors: Lin Xiang
Xiaoqin Zeng
Shengli Wu
Yanjun Liu
Baohua Yuan
Publication date: 03-01-2021
Publisher: Springer US
Published in: Neural Processing Letters / Issue 1/2021
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-020-10420-7

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