We propose a simple yet powerful ResNet ensemble algorithm which consists of two components: First, we modify the base ResNet by adding variance specified Gaussian noise to the output of each original residual mapping. Second, we average over the production of multiple parallel and jointly trained modified ResNets to get the final prediction. Heuristically, these two simple steps give an approximation to the well-known Feynman-Kac formula for representing the solution of a transport equation with viscosity, or a convection-diffusion equation. This simple ensemble algorithm improves neural nets' generalizability and robustness towards adversarial attack. In particular, for the CIFAR10 benchmark, with the projected gradient descent adversarial training, we show that even an ensemble of two ResNet20 leads to a 5$\%$ higher accuracy towards the strongest iterative fast gradient sign attack than the state-of-the-art adversarial defense algorithm.

提出了一种基于传输方程最优控制理论的 ResNets 集合算法，该算法通过给每个残差映射的输出添加方差指定的高斯噪声的方式修改基本 ResNets 算法，并通过平均多个经过联合训练的修改后的 ResNets 产生的预测结果来提高抵抗 IFGSM 攻击的模型的预测准确率，该算法在 CIFAR10 基准测试中表现出相对于当前领先的防御 IFGSM 攻击的模型而言更高的训练鲁棒性以及自然准确性。

利用 Feynman-Kac 形式的 ResNets 集成来提高自然和鲁棒的准确性