论文标题
贝叶斯神经网络的概率安全
Probabilistic Safety for Bayesian Neural Networks
论文作者
论文摘要
我们研究了在对抗输入扰动下贝叶斯神经网络（BNN）的概率安全性。给定一组紧凑的输入点，$ t \ subseteq \ mathbb {r}^m $，我们研究概率W.R.T. $ t $中所有点的BNN后部映射到输出空间中的同一区域$ s $。特别是，这可以用来评估从BNN采样的网络很容易受到对抗性攻击的可能性。我们依靠从非凸优化的放松技术来开发一种计算BNN概率安全性下限的方法，从而为间隔和线性功能传播技术的情况提供了明确的程序。我们将方法应用于接受回归任务，空中碰撞和MNIST训练的BNN，从经验上表明，我们的方法允许人们证明具有数百万参数的BNN的概率安全性。
We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply our methods to BNNs trained on a regression task, airborne collision avoidance, and MNIST, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.
