Multivariate Lipschitz Analysis of the Stability of Neural Networks

The stability of neural networks with respect to adversarial perturbations has been extensively studied. One the main strategies consist quantifying Lipschitz regularity networks. In this paper, we introduce a multivariate constant-based analysis fully connected allowing us capture influence each input or group inputs on network stability. Our approach relies suitable re-normalization space, objective perform more precise than one provided by global constant. We investigate mathematical properties proposed and show its usefulness in better understanding sensitivity regard groups inputs. display results new representation designed for machine learning practitioners safety engineers termed as star. star is graphical practical tool analyze model during development, different combinations By leveraging tool, that it possible build robust-by-design models using spectral normalization techniques controlling network, given target. Thanks our analysis, can also measure efficiency training inference tasks. experiments various open access tabular datasets, real Thales Air Mobility industrial application subject certification requirements.