Robustness of Neural Networks: A Probabilistic and Practical Approach

The researchers propose probabilistic robustness, a new definition of neural network robustness, requiring the network to remain robust with probability at least (1-ε) under a given input distribution. The paper notes that existing robustness definitions mostly focus on the worst case of adversarial inputs, which is too strict, making it difficult for actual neural networks to satisfy and verify, whereas real-world inputs come from non-adversarial probability distributions. The authors also provide a verification algorithm based on abstract interpretation and importance sampling: first use abstract interpretation to approximate network behavior and over-approximate the input regions that violate robustness, then use importance sampling to offset the effect of over-approximation and estimate the probability that the network violates the robustness property, providing a practical and principled method for robustness estimation.