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Special Issue:
SPECIAL TOPIC — Machine learning in statistical physics
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| SPECIAL TOPIC—Machine learning in statistical physics |
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Relationship between manifold smoothness and adversarial vulnerability in deep learning with local errors |
| Zijian Jiang(蒋子健), Jianwen Zhou(周健文), and Haiping Huang(黄海平)† |
| 1 PMI Laboratory, School of Physics, Sun Yat-sen University, Guangzhou 510275, China |
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Abstract Artificial neural networks can achieve impressive performances, and even outperform humans in some specific tasks. Nevertheless, unlike biological brains, the artificial neural networks suffer from tiny perturbations in sensory input, under various kinds of adversarial attacks. It is therefore necessary to study the origin of the adversarial vulnerability. Here, we establish a fundamental relationship between geometry of hidden representations (manifold perspective) and the generalization capability of the deep networks. For this purpose, we choose a deep neural network trained by local errors, and then analyze emergent properties of the trained networks through the manifold dimensionality, manifold smoothness, and the generalization capability. To explore effects of adversarial examples, we consider independent Gaussian noise attacks and fast-gradient-sign-method (FGSM) attacks. Our study reveals that a high generalization accuracy requires a relatively fast power-law decay of the eigen-spectrum of hidden representations. Under Gaussian attacks, the relationship between generalization accuracy and power-law exponent is monotonic, while a non-monotonic behavior is observed for FGSM attacks. Our empirical study provides a route towards a final mechanistic interpretation of adversarial vulnerability under adversarial attacks.
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Received: 09 July 2020
Revised: 09 December 2020
Accepted manuscript online: 24 December 2020
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PACS:
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87.18.Sn
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(Neural networks and synaptic communication)
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87.19.lv
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(Learning and memory)
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| Fund: Project supported by the National Key R&D Program of China (Grant No. 2019YFA0706302), the start-up budget 74130-18831109 of the 100-talent-program of Sun Yat-sen University, and the National Natural Science Foundation of China (Grant No. 11805284). |
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Corresponding Authors:
†Corresponding author. E-mail: huanghp7@mail.sysu.edu.cn
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Cite this article:
Zijian Jiang(蒋子健), Jianwen Zhou(周健文), and Haiping Huang(黄海平) Relationship between manifold smoothness and adversarial vulnerability in deep learning with local errors 2021 Chin. Phys. B 30 048702
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1 Goodfellow I, Bengio Y and Courville A2016 Deep Learning (Cambridge, MA: MIT Press)
2 Carlini N and Wagner D 2017 IEEE Symposium on Security and Privacy (SP), pp. 39-57
3 Su J W, Vargas D V and Sakurai K 2019 IEEE Transactions on Evolutionary Computation 23 828
4 Zhou Z L and Firestone C 2019 Nat. Commun. 10 1334
5 Stringer C, Pachitariu M, Steinmetz N, Carandini M and Harris K D 2019 Nature 571 361
6 Mostafa H, Ramesh V and Cauwenberghs G 2018 Frontiers in Neuroscience 12 608
7 Lillicrap T P, Santoro A, Marris L, Akerman C J and Hinton G 2020 Nature Reviews Neuroscience 21 335
8 Yamins D L K and DiCarlo J 2016 Nat. Neurosci. 19 356
9 Lecun Y, Bottou L, Bengio Y and Haffner P 1998 Proc. IEEE 86 2278
10 Szegedy C, Zaremba W, Sutskever I, Bruna J, Erhan D, Goodfellow I and Fergus R 2014 International Conference on Learning Representations (ICLR)
11 Goodfellow I, Shlens J and Szegedy C 2015 International Conference on Learning Representations (ICLR)
12 Huang H P 2018 Phys. Rev. E 98 062313
13 Zhou J W and Huang H P 2021 Phys. Rev. E 103 012315 |
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