论文标题
使用多项式Zonotopes开放和闭环神经网络验证
Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes
论文作者
论文摘要
我们提出了一种新的方法，可以通过具有relu，sigmoid或双曲线切线激活功能的神经网络有效计算图像的紧密非凸面。特别是，我们通过多项式近似来抽象每个神经元的输入输出关系，该近似是使用多项式界定的基于设定的方式进行评估的。虽然我们的方法也可能对开环神经网络验证有益，但我们的主要应用是对神经网络控制系统的可及性分析，在该系统中多项式界限能够捕获由神经网络以及系统动力学引起的非共识性。与其他方法相比，这与其他基准相比，这会产生卓越的性能。
We present a novel approach to efficiently compute tight non-convex enclosures of the image through neural networks with ReLU, sigmoid, or hyperbolic tangent activation functions. In particular, we abstract the input-output relation of each neuron by a polynomial approximation, which is evaluated in a set-based manner using polynomial zonotopes. While our approach can also can be beneficial for open-loop neural network verification, our main application is reachability analysis of neural network controlled systems, where polynomial zonotopes are able to capture the non-convexity caused by the neural network as well as the system dynamics. This results in a superior performance compared to other methods, as we demonstrate on various benchmarks.
