Exponential Activation Function

Exponential activation functions are gaining traction in neural networks, offering unique properties compared to more common functions like ReLU. Current research explores their use in diverse applications, including over-parameterized regression models and control systems operating on manifolds like SE(3), often employing gradient descent optimization and leveraging matrix exponential calculations. This renewed interest stems from their potential to improve model expressiveness and address limitations in existing architectures, particularly in areas like large language models and diffeomorphic image registration where maintaining positive Jacobians is crucial. The development of efficient algorithms for computing matrix exponentials and their derivatives is a key focus, enabling applications in complex systems like stochastic epidemic modeling.