Tight Verification of Probabilistic Robustness in Bayesian Neural Networks
This work addresses the verification challenge for BNNs, which is crucial for ensuring safety in applications like autonomous systems, but it is incremental as it builds on existing verification methods.
The paper tackles the problem of verifying probabilistic robustness in Bayesian Neural Networks (BNNs), which is more challenging than for standard neural networks due to the need to search parameter spaces for safe weights, and introduces two algorithms that compute bounds up to 40% tighter than the state-of-the-art on benchmarks like MNIST and CIFAR10.
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.