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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2511.11699 |
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| _version_ | 1866912710231326720 |
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| author | Lin, Xingqi Chen, Liangyu Wu, Min Zhang, Min Zeng, Zhenbing |
| author_facet | Lin, Xingqi Chen, Liangyu Wu, Min Zhang, Min Zeng, Zhenbing |
| contents | Robustness verification is a promising technique for rigorously proving Recurrent Neural Networks (RNNs) robustly. A key challenge is to over-approximate the nonlinear activation functions with linear constraints, which can transform the verification problem into an efficiently solvable linear programming problem. Existing methods over-approximate the nonlinear parts with linear bounding planes individually, which may cause significant over-estimation and lead to lower verification accuracy. In this paper, in order to tightly enclose the three-dimensional nonlinear surface generated by the Hadamard product, we propose a novel truncated rectangular prism formed by two linear relaxation planes and a refinement-driven method to minimize both its volume and surface area for tighter over-approximation. Based on this approximation, we implement a prototype DeepPrism for RNN robustness verification. The experimental results demonstrate that \emph{DeepPrism} has significant improvement compared with the state-of-the-art approaches in various tasks of image classification, speech recognition and sentiment analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verification Lin, Xingqi Chen, Liangyu Wu, Min Zhang, Min Zeng, Zhenbing Machine Learning Robustness verification is a promising technique for rigorously proving Recurrent Neural Networks (RNNs) robustly. A key challenge is to over-approximate the nonlinear activation functions with linear constraints, which can transform the verification problem into an efficiently solvable linear programming problem. Existing methods over-approximate the nonlinear parts with linear bounding planes individually, which may cause significant over-estimation and lead to lower verification accuracy. In this paper, in order to tightly enclose the three-dimensional nonlinear surface generated by the Hadamard product, we propose a novel truncated rectangular prism formed by two linear relaxation planes and a refinement-driven method to minimize both its volume and surface area for tighter over-approximation. Based on this approximation, we implement a prototype DeepPrism for RNN robustness verification. The experimental results demonstrate that \emph{DeepPrism} has significant improvement compared with the state-of-the-art approaches in various tasks of image classification, speech recognition and sentiment analysis. |
| title | Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.11699 |