Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verification
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| Format: | Preprint |
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2025
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| author | Marzari, Luca Cicalese, Ferdinando Farinelli, Alessandro |
| author_facet | Marzari, Luca Cicalese, Ferdinando Farinelli, Alessandro |
| contents | We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from LiRPA-based approaches with a sampling-based method to compute tight intermediate reachable sets. In detail, we show that with negligible computational overhead, $\texttt{PT-LiRPA}$ exploiting the estimated reachable sets, significantly tightens the lower and upper linear bounds of a neural network's output, reducing the computational cost of formal verification tools while providing probabilistic guarantees on verification soundness. Extensive experiments on standard formal verification benchmarks, including the International Verification of Neural Networks Competition, show that our $\texttt{PT-LiRPA}$-based verifier improves robustness certificates, i.e., the certified lower bound of $\varepsilon$ perturbation tolerated by the models, by up to 3.31X and 2.26X compared to related work. Importantly, our probabilistic approach results in a valuable solution for challenging competition entries where state-of-the-art formal verification methods fail, allowing us to provide answers with high confidence (i.e., at least 99%). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_05405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verification Marzari, Luca Cicalese, Ferdinando Farinelli, Alessandro Machine Learning Artificial Intelligence We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from LiRPA-based approaches with a sampling-based method to compute tight intermediate reachable sets. In detail, we show that with negligible computational overhead, $\texttt{PT-LiRPA}$ exploiting the estimated reachable sets, significantly tightens the lower and upper linear bounds of a neural network's output, reducing the computational cost of formal verification tools while providing probabilistic guarantees on verification soundness. Extensive experiments on standard formal verification benchmarks, including the International Verification of Neural Networks Competition, show that our $\texttt{PT-LiRPA}$-based verifier improves robustness certificates, i.e., the certified lower bound of $\varepsilon$ perturbation tolerated by the models, by up to 3.31X and 2.26X compared to related work. Importantly, our probabilistic approach results in a valuable solution for challenging competition entries where state-of-the-art formal verification methods fail, allowing us to provide answers with high confidence (i.e., at least 99%). |
| title | Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verification |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2507.05405 |