Set-Based Training for Neural Network Verification
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908478855970816 |
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| author | Koller, Lukas Ladner, Tobias Althoff, Matthias |
| author_facet | Koller, Lukas Ladner, Tobias Althoff, Matthias |
| contents | Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness of a neural network must be formally verified against input perturbations, e.g., from noisy sensors. To improve the robustness of neural networks and thus simplify the formal verification, we present a novel set-based training procedure in which we compute the set of possible outputs given the set of possible inputs and compute for the first time a gradient set, i.e., each possible output has a different gradient. Therefore, we can directly reduce the size of the output enclosure by choosing gradients toward its center. Small output enclosures increase the robustness of a neural network and, at the same time, simplify its formal verification. The latter benefit is due to the fact that a larger size of propagated sets increases the conservatism of most verification methods. Our extensive evaluation demonstrates that set-based training produces robust neural networks with competitive performance, which can be verified using fast (polynomial-time) verification algorithms due to the reduced output set. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_14961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Set-Based Training for Neural Network Verification Koller, Lukas Ladner, Tobias Althoff, Matthias Machine Learning Cryptography and Security Logic in Computer Science Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness of a neural network must be formally verified against input perturbations, e.g., from noisy sensors. To improve the robustness of neural networks and thus simplify the formal verification, we present a novel set-based training procedure in which we compute the set of possible outputs given the set of possible inputs and compute for the first time a gradient set, i.e., each possible output has a different gradient. Therefore, we can directly reduce the size of the output enclosure by choosing gradients toward its center. Small output enclosures increase the robustness of a neural network and, at the same time, simplify its formal verification. The latter benefit is due to the fact that a larger size of propagated sets increases the conservatism of most verification methods. Our extensive evaluation demonstrates that set-based training produces robust neural networks with competitive performance, which can be verified using fast (polynomial-time) verification algorithms due to the reduced output set. |
| title | Set-Based Training for Neural Network Verification |
| topic | Machine Learning Cryptography and Security Logic in Computer Science |
| url | https://arxiv.org/abs/2401.14961 |