LEVIS: Large Exact Verifiable Input Spaces for Neural Networks

• URL: http://arxiv.org/abs/2408.08824v1
• Date: Fri, 16 Aug 2024 16:15:57 GMT
• Title: LEVIS: Large Exact Verifiable Input Spaces for Neural Networks
• Authors: Mohamad Fares El Hajj Chehade, Brian Wesley Bell, Russell Bent, Hao Zhu, Wenting Li,
• Abstract summary: robustness of neural networks is paramount in safety-critical applications. We introduce a novel framework, $textttLEVIS$, comprising $textttLEVIS$-$beta$. We offer a theoretical analysis elucidating the properties of the verifiable balls acquired through $textttLEVIS$-$alpha$ and $textttLEVIS$-$beta$.
• Score: 8.673606921201442
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The robustness of neural networks is paramount in safety-critical applications. While most current robustness verification methods assess the worst-case output under the assumption that the input space is known, identifying a verifiable input space $\mathcal{C}$, where no adversarial examples exist, is crucial for effective model selection, robustness evaluation, and the development of reliable control strategies. To address this challenge, we introduce a novel framework, $\texttt{LEVIS}$, comprising $\texttt{LEVIS}$-$\alpha$ and $\texttt{LEVIS}$-$\beta$. $\texttt{LEVIS}$-$\alpha$ locates the largest possible verifiable ball within the central region of $\mathcal{C}$ that intersects at least two boundaries. In contrast, $\texttt{LEVIS}$-$\beta$ integrates multiple verifiable balls to encapsulate the entirety of the verifiable space comprehensively. Our contributions are threefold: (1) We propose $\texttt{LEVIS}$ equipped with three pioneering techniques that identify the maximum verifiable ball and the nearest adversarial point along collinear or orthogonal directions. (2) We offer a theoretical analysis elucidating the properties of the verifiable balls acquired through $\texttt{LEVIS}$-$\alpha$ and $\texttt{LEVIS}$-$\beta$. (3) We validate our methodology across diverse applications, including electrical power flow regression and image classification, showcasing performance enhancements and visualizations of the searching characteristics.

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