用更紧的立体棱柱逼近RNN非线性层，提升鲁棒性验证精度。
Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verification
- 用双平面+优化方法构造截断长方体，紧密包裹哈达玛积生成的三维曲面。
- 在图像分类、语音识别和情感分析任务中，验证准确率显著优于现有方法。
- 适合需要严格证明RNN鲁棒性的研究者，尤其关注可信AI与安全验证场景。
鲁棒性验证是严格证明循环神经网络（RNNs）鲁棒性的有力技术。核心挑战在于用线性约束过估计非线性激活函数，从而将验证问题转化为可高效求解的线性规划问题。现有方法对非线性部分逐个使用线性边界平面进行过估计，可能导致严重高估，降低验证精度。本文为更紧密地包裹由哈达玛积生成的三维非线性曲面，提出一种新型截断长方体，由两个线性松弛平面及一种基于精化驱动的方法构成，以最小化其体积与表面积。基于此近似，我们实现了一个原型系统 DeepPrism，用于RNN鲁棒性验证。实验结果表明，DeepPrism 在图像分类、语音识别和情感分析等多种任务中均显著优于当前最优方法。
原文摘要 · Abstract (English)
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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