  Convolutional neural networks (CNNs), one of the key architectures of deep
learning models, have achieved superior performance on many machine learning
tasks such as image classification, video recognition, and power systems.
Despite their success, CNNs can be easily contaminated by natural noises and
artificially injected noises such as backdoor attacks. In this paper, we
propose a robust recovery method to remove the noise from the potentially
contaminated CNNs and provide an exact recovery guarantee on one-hidden-layer
non-overlapping CNNs with the rectified linear unit (ReLU) activation function.
Our theoretical results show that both CNNs' weights and biases can be exactly
recovered under the overparameterization setting with some mild assumptions.
The experimental results demonstrate the correctness of the proofs and the
effectiveness of the method in both the synthetic environment and the practical
neural network setting. Our results also indicate that the proposed method can
be extended to multiple-layer CNNs and potentially serve as a defense strategy
against backdoor attacks.
