Enhancing Backdoor Attacks with Multi-Level MMD Regularization

While Deep Neural Networks (DNNs) excel in many tasks, the huge training resources they require become an obstacle for practitioners to develop their own models. It has become common to collect data from the Internet or hire a third party to train models. Unfortunately, recent studies have shown that these operations provide a viable pathway for maliciously injecting hidden backdoors into DNNs. Several defense methods have been developed to detect malicious samples, with the common assumption that the latent representations of benign and malicious samples extracted by the infected model exhibit different distributions. However, a comprehensive study on the distributional differences is missing. In this paper, we investigate such differences thoroughly via answering three questions: 1) What are the characteristics of the distributional differences? 2) How can they be effectively reduced? 3) What impact does this reduction have on difference-based defense methods? First, the distributional differences of multi-level representations on the regularly trained backdoored models are verified to be significant by introducing Maximum Mean Discrepancy (MMD), Energy Distance (ED), and Sliced Wasserstein Distance (SWD) as the metrics. Then, ML-MMDR, a difference reduction method that adds multi-level MMD regularization into the loss, is proposed, and its effectiveness is testified on three typical difference-based defense methods. Across all the experimental settings, the F1 scores of these methods drop from 90%-100% on the regularly trained backdoored models to 60%-70% on the models trained with ML-MMDR. These results indicate that the proposed MMD regularization can enhance the stealthiness of existing backdoor attack methods. The prototype code of our method is now available at https://github.com/xpf/Multi-Level-MMD-Regularization.