用混合区间数提升卷积神经网络可达性分析效率
Efficient Reachability Analysis for Convolutional Neural Networks Using Hybrid Zonotopes
- 采用混合区间数表示输出集合，兼顾精度与速度
- 在多个测试数据集上实现更快的计算且误差可控
- 适合安全关键系统中神经网络的快速验证
前馈神经网络广泛应用于自动驾驶系统中的控制与感知任务，但其对对抗攻击的脆弱性要求在部署于安全关键应用前必须进行形式化验证。现有的基于集合传播的前馈神经网络可达性分析方法往往难以同时实现可扩展性和高精度。本文提出一种新型基于集合的方法，用于计算卷积神经网络的可达集合。该方法利用混合区间数表示和高效的神经网络简化技术，在计算复杂度与近似精度之间提供灵活权衡。通过数值实验验证了所提方法的有效性。
原文摘要 · Abstract (English)
Feedforward neural networks are widely used in autonomous systems, particularly for control and perception tasks within the system loop. However, their vulnerability to adversarial attacks necessitates formal verification before deployment in safety-critical applications. Existing set propagation-based reachability analysis methods for feedforward neural networks often struggle to achieve both scalability and accuracy. This work presents a novel set-based approach for computing the reachable sets of convolutional neural networks. The proposed method leverages a hybrid zonotope representation and an efficient neural network reduction technique, providing a flexible trade-off between computational complexity and approximation accuracy. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.
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