Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verification

• URL: http://arxiv.org/abs/2511.11699v1
• Date: Wed, 12 Nov 2025 12:27:19 GMT
• Title: Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verification
• Authors: Xingqi Lin, Liangyu Chen, Min Wu, Min Zhang, Zhenbing Zeng,
• Abstract summary: Robustness verification is a promising technique for rigorously proving Recurrent Neural Networks (RNNs) robustly.<n>Existing methods over-approximate the nonlinear parts with linear bounding planes individually, which may cause significant over-estimation and lead to lower verification accuracy.<n>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.
• Score: 19.808988000317616
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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