Tight Verification of Probabilistic Robustness in Bayesian Neural Networks
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| Format: | Preprint |
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2024
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| _version_ | 1866913247511183360 |
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| author | Batten, Ben Hosseini, Mehran Lomuscio, Alessio |
| author_facet | Batten, Ben Hosseini, Mehran Lomuscio, Alessio |
| contents | We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness of standard Neural Networks (NNs) because it requires searching the parameters' space for safe weights. Moreover, tight and complete approaches for the verification of standard NNs, such as those based on Mixed-Integer Linear Programming (MILP), cannot be directly used for the verification of BNNs because of the polynomial terms resulting from the consecutive multiplication of variables encoding the weights. Our algorithms efficiently and effectively search the parameters' space for safe weights by using iterative expansion and the network's gradient and can be used with any verification algorithm of choice for BNNs. In addition to proving that our algorithms compute tighter bounds than the SoA, we also evaluate our algorithms against the SoA on standard benchmarks, such as MNIST and CIFAR10, showing that our algorithms compute bounds up to 40% tighter than the SoA. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_11627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tight Verification of Probabilistic Robustness in Bayesian Neural Networks Batten, Ben Hosseini, Mehran Lomuscio, Alessio Machine Learning Artificial Intelligence Formal Languages and Automata Theory Logic in Computer Science 68T27 (Primary) 68T45, 68T07, 68T01 (Secondary) I.2.0; I.2.4; F.3.1; D.2.4 We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness of standard Neural Networks (NNs) because it requires searching the parameters' space for safe weights. Moreover, tight and complete approaches for the verification of standard NNs, such as those based on Mixed-Integer Linear Programming (MILP), cannot be directly used for the verification of BNNs because of the polynomial terms resulting from the consecutive multiplication of variables encoding the weights. Our algorithms efficiently and effectively search the parameters' space for safe weights by using iterative expansion and the network's gradient and can be used with any verification algorithm of choice for BNNs. In addition to proving that our algorithms compute tighter bounds than the SoA, we also evaluate our algorithms against the SoA on standard benchmarks, such as MNIST and CIFAR10, showing that our algorithms compute bounds up to 40% tighter than the SoA. |
| title | Tight Verification of Probabilistic Robustness in Bayesian Neural Networks |
| topic | Machine Learning Artificial Intelligence Formal Languages and Automata Theory Logic in Computer Science 68T27 (Primary) 68T45, 68T07, 68T01 (Secondary) I.2.0; I.2.4; F.3.1; D.2.4 |
| url | https://arxiv.org/abs/2401.11627 |