Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise
This work addresses the problem of stabilizing and regularizing continuous neural networks for researchers and practitioners in machine learning, though it is incremental as it builds directly on Neural ODE.
The authors tackled the lack of regularization mechanisms like dropout and noise injection in Neural ODE networks by proposing Neural SDE, a framework that incorporates stochastic noise for improved robustness and generalization. They demonstrated that Neural SDE achieves better generalization than Neural ODE and is more resistant to adversarial and non-adversarial perturbations.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous neural network framework called Neural Stochastic Differential Equation (Neural SDE) network, which naturally incorporates various commonly used regularization mechanisms based on random noise injection. Our framework can model various types of noise injection frequently used in discrete networks for regularization purpose, such as dropout and additive/multiplicative noise in each block. We provide theoretical analysis explaining the improved robustness of Neural SDE models against input perturbations/adversarial attacks. Furthermore, we demonstrate that the Neural SDE network can achieve better generalization than the Neural ODE and is more resistant to adversarial and non-adversarial input perturbations.