Backdoor Learning Curves: Explaining Backdoor Poisoning Beyond Influence Functions

Backdoor attacks inject poisoning samples during training, with the goal of enforcing a machine-learning model to output an attacker-chosen class when presented a specific trigger at test time. Although backdoor attacks have been demonstrated in a variety of settings and against different models, the factors affecting their success are not yet well understood. In this work, we provide a unifying framework to study the process of backdoor learning under the lens of incremental learning and influence functions. We show that the success of backdoor attacks inherently depends on (i) the complexity of the learning algorithm, controlled by its hyperparameters, and (ii) the fraction of backdoor samples injected into the training set. These factors affect how fast a machine-learning model learns to correlate the presence of a backdoor trigger with the target class. Interestingly, our analysis shows that there exists a region in the hyperparameter space in which the accuracy on clean test samples is still high while backdoor attacks become ineffective, thereby suggesting novel criteria to improve existing defenses.