Local Linearity

Local linearity, the approximation of complex nonlinear systems using linear models within localized regions, is a key concept across diverse scientific fields. Current research focuses on leveraging this principle in deep learning, particularly for improving the interpretability of neural networks, enhancing the stability of adversarial training, and enabling efficient system identification and control in dynamical systems like those found in orbital mechanics. These advancements are significant because they address challenges in model robustness, uncertainty quantification, and the development of more efficient and interpretable AI models, with applications ranging from aerospace engineering to biological systems modeling.