Measuring Neural Network Robustness to Input Noise

The robustness of neural networks to perturbations in their input data is a critical concern, particularly when dealing with real-world noise. This research focuses on understanding the interplay between a network's accuracy, typically measured by mean squared error, and its ability to withstand random noise. A key contribution is the introduction of a novel robustness measure. This proposed measure is designed to be both simple and computationally efficient, treating the neural network as a black box. With high probability, it provides an upper bound on the network's mean squared error for a given dataset and input perturbation level. Experimental results across several real-world datasets demonstrate the efficacy of this method. Furthermore, the paper introduces the concept of "robustness curves." These curves offer a visual and analytical tool to further examine and compare the robustness characteristics of neural networks, both within a single dataset under varying noise levels and when comparing performance across different datasets. This allows for a more nuanced understanding of a model's resilience.