  Recent studies have shown that Deep Neural Networks (DNNs) are vulnerable to
the backdoor attacks, which leads to malicious behaviors of DNNs when specific
triggers are attached to the input images. It was further demonstrated that the
infected DNNs possess a collection of channels, which are more sensitive to the
backdoor triggers compared with normal channels. Pruning these channels was
then shown to be effective in mitigating the backdoor behaviors. To locate
those channels, it is natural to consider their Lipschitzness, which measures
their sensitivity against worst-case perturbations on the inputs. In this work,
we introduce a novel concept called Channel Lipschitz Constant (CLC), which is
defined as the Lipschitz constant of the mapping from the input images to the
output of each channel. Then we provide empirical evidences to show the strong
correlation between an Upper bound of the CLC (UCLC) and the trigger-activated
change on the channel activation. Since UCLC can be directly calculated from
the weight matrices, we can detect the potential backdoor channels in a
data-free manner, and do simple pruning on the infected DNN to repair the
model. The proposed Channel Lipschitzness based Pruning (CLP) method is super
fast, simple, data-free and robust to the choice of the pruning threshold.
Extensive experiments are conducted to evaluate the efficiency and
effectiveness of CLP, which achieves state-of-the-art results among the
mainstream defense methods even without any data. Source codes are available at
https://github.com/rkteddy/channel-Lipschitzness-based-pruning.
