# Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verification

arXiv: https://arxiv.org/abs/2511.11699 · HTML: https://mlsanity.com/paper/2511.11699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Crafting Adversarial Input Sequences for Recurrent Neural Networks](https://mlsanity.com/paper/1604.08275/) (2016)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [POPQORN: Quantifying Robustness of Recurrent Neural Networks](https://mlsanity.com/paper/1905.07387/) (2019)
- [Efficient Neural Network Analysis with Sum-of-Infeasibilities](https://mlsanity.com/paper/2203.11201/) (2022)
- [Scalable Polyhedral Verification of Recurrent Neural Networks](https://mlsanity.com/paper/2005.13300/) (2020)
- [DiffRNN: Differential Verification of Recurrent Neural Networks](https://mlsanity.com/paper/2007.10135/) (2020)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Advancing Neural Network Verification through Hierarchical Safety Abstract Interpretation](https://mlsanity.com/paper/2505.05235/) (2025)
- [PICID: Proof-Driven Clause Learning in Neural Network Verification](https://mlsanity.com/paper/2503.12083/) (2025)

## Abstract (arXiv)

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 DeepPrism has significant improvement compared with the state-of-the-art approaches in various tasks of image classification, speech recognition and sentiment analysis.