Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917581745553408 |
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| author | Fu, Shaopeng Wang, Di |
| author_facet | Fu, Shaopeng Wang, Di |
| contents | Adversarial training (AT) is a canonical method for enhancing the robustness of deep neural networks (DNNs). However, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time AT can be detrimental to the robustness of DNNs. This paper presents a theoretical explanation of robust overfitting for DNNs. Specifically, we non-trivially extend the neural tangent kernel (NTK) theory to AT and prove that an adversarially trained wide DNN can be well approximated by a linearized DNN. Moreover, for squared loss, closed-form AT dynamics for the linearized DNN can be derived, which reveals a new AT degeneration phenomenon: a long-term AT will result in a wide DNN degenerates to that obtained without AT and thus cause robust overfitting. Based on our theoretical results, we further design a method namely Adv-NTK, the first AT algorithm for infinite-width DNNs. Experiments on real-world datasets show that Adv-NTK can help infinite-width DNNs enhance comparable robustness to that of their finite-width counterparts, which in turn justifies our theoretical findings. The code is available at https://github.com/fshp971/adv-ntk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06112 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach Fu, Shaopeng Wang, Di Machine Learning Adversarial training (AT) is a canonical method for enhancing the robustness of deep neural networks (DNNs). However, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time AT can be detrimental to the robustness of DNNs. This paper presents a theoretical explanation of robust overfitting for DNNs. Specifically, we non-trivially extend the neural tangent kernel (NTK) theory to AT and prove that an adversarially trained wide DNN can be well approximated by a linearized DNN. Moreover, for squared loss, closed-form AT dynamics for the linearized DNN can be derived, which reveals a new AT degeneration phenomenon: a long-term AT will result in a wide DNN degenerates to that obtained without AT and thus cause robust overfitting. Based on our theoretical results, we further design a method namely Adv-NTK, the first AT algorithm for infinite-width DNNs. Experiments on real-world datasets show that Adv-NTK can help infinite-width DNNs enhance comparable robustness to that of their finite-width counterparts, which in turn justifies our theoretical findings. The code is available at https://github.com/fshp971/adv-ntk. |
| title | Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2310.06112 |