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Computation of CNN’s Sensitivity to Input Perturbation

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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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Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities under Grant Nos. 2016B44414 and 2018B678X14, Postgraduate Research and Practice Innovation Program of Jiangsu Province of China under Grant No. KYCX18_0553, and the Science and Technology Project of Huai’an City under Grant No. HAG201602 and HAS201607.

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Authors and Affiliations

  1. Institute of Intelligence Science and Technology, Hohai University, Nanjing, China

    Lin Xiang, Xiaoqin Zeng, Yanjun Liu & Baohua Yuan

  2. Huaiyin Institute of Technology, Huai’an, China

    Lin Xiang

  3. School of Computing, Ulster University, Belfast, UK

    Shengli Wu

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  1. Lin Xiang
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  2. Xiaoqin Zeng
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  3. Shengli Wu
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Correspondence to Xiaoqin Zeng.

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Xiang, L., Zeng, X., Wu, S. et al. Computation of CNN’s Sensitivity to Input Perturbation. Neural Process Lett 53, 535–560 (2021). https://doi.org/10.1007/s11063-020-10420-7

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