We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness of standard Neural Networks (NNs) because it requires searching the parameters' space for safe weights. Moreover, tight and complete approaches for the verification of standard NNs, such as those based on Mixed-Integer Linear Programming (MILP), cannot be directly used for the verification of BNNs because of the polynomial terms resulting from the consecutive multiplication of variables encoding the weights. Our algorithms efficiently and effectively search the parameters' space for safe weights by using iterative expansion and the network's gradient and can be used with any verification algorithm of choice for BNNs. In addition to proving that our algorithms compute tighter bounds than the SoA, we also evaluate our algorithms against the SoA on standard benchmarks, such as MNIST and CIFAR10, showing that our algorithms compute bounds up to 40% tighter than the SoA.

翻译：我们提出了两种算法，用于计算贝叶斯神经网络（BNNs）概率鲁棒性的严格保证。与验证标准神经网络（NNs）的鲁棒性相比，计算BNNs的鲁棒性保证是一项更具挑战性的任务，因为它需要在参数空间中搜索安全的权重。此外，标准神经网络验证中的严格且完备的方法（例如基于混合整数线性规划（MILP）的方法）无法直接用于验证BNNs，原因在于编码权重的变量连续相乘会产生多项式项。我们的算法通过使用迭代扩展和网络梯度，高效且有效地在参数空间中搜索安全权重，并且可与任何针对BNNs的验证算法结合使用。除了证明我们的算法比现有技术（SoA）计算更紧的边界外，我们还在标准基准测试（如MNIST和CIFAR10）上对算法与SoA进行了评估，结果显示，我们计算的边界比SoA紧上高达40%。