# Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise

## TL;DR

This paper introduces Neural SDE, a stochastic extension of Neural ODEs, incorporating noise-based regularization techniques to improve robustness and generalization against adversarial attacks.

## Contribution

It proposes Neural SDE, a novel framework that integrates noise regularization into Neural ODEs, enhancing robustness and generalization capabilities.

## Key findings

- Neural SDE models are more robust to input perturbations.
- Neural SDE achieves better generalization than Neural ODE.
- Neural SDE resists adversarial attacks more effectively.

## Abstract

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.