When Stronger Triggers Backfire: A High-Dimensional Theory of Backdoor Attacks

Despite recent progress in backdoor attacks, existing methods remain susceptible to post-training defenses that erase the backdoor through fine-tuning or pruning. We revisit the core objectives of backdoor attacks and derive principled criteria characterizing optimal sample-specific trigger construction under a Bayes-optimal model of the victim's training. Our analysis reveals that both attack success and clean-accuracy preservation are simultaneously optimized when triggered samples are steered into low-density regions of the clean data distribution, a distributional condition that controls all moments of the poisoned distribution at once rather than a handful of input-space summary statistics. We introduce a bilevel optimization framework that estimates density ratios via conditional time-score matching and optimizes a mixture-model objective to place triggered samples in these sparse regions. Extensive evaluations on MNIST, CIFAR-10, GTSRB, and TinyImageNet demonstrate that our method achieves above 99% attack success rate before defense and retains 50--85 percentage points higher post-defense ASR than the strongest baselines under fine-tuning defenses. Against neuron-pruning defenses, the method exhibits complete immunity, with zero neurons identified for removal across all pruning thresholds. These results expose a fundamental gap in current defense paradigms and underscore the need for defenses that operate beyond the support of the clean distribution.

Machine-learning services increasingly rely on public data, third-party providers, and outsourced training, creating opportunities for data-poisoning attacks that implant persistent malicious behavior while preserving benign utility. However, existing backdoor studies largely evaluate exact trigger reuse, training-exposed trigger diversity, or variations along predefined transformation axes. They therefore leave a critical blind spot: whether a backdoor learned from one training-time trigger can generalize to an inference-time trigger family absent from victim training. We formulate this problem as backdoor generalization under training--inference trigger shift and introduce Lilith, a black-box anchor-to-family framework. Using only disjoint surrogate resources, Lilith first induces a compact target-side vulnerability with a single training anchor, then constructs a bounded inference-only family that preserves the anchor-induced representation geometry. We characterize this mechanism through anchor clearance and family reach, deriving sufficient conditions for family-wise target preservation under local regularity and bounded surrogate--victim discrepancy. Experiments across datasets, architectures, poisoning rates, and defenses show that Lilith achieves high family-wise attack success with limited utility degradation and a small trigger generalization gap. Additional analyses show that family activation depends on representation alignment rather than the proposal mechanism, exposing a broader threat overlooked by exact-trigger evaluation.

Data poisoning corrupts training data to degrade a model or to plant attacker-controlled behavior. This study evaluates two representative training-time attacks, label flipping and backdoor poisoning, on MNIST and Fashion-MNIST with three baseline classifiers: Logistic Regression, Linear SVM, and Random Forest. Clean training is compared with poisoning rates of 5%, 10%, and 20% using clean-test accuracy, macro-precision, macro-recall, macro-F1, and, for backdoors, attack success rate. Label flipping caused clear degradation, largest for Logistic Regression and Linear SVM, while Random Forest stayed comparatively stable. Backdoor poisoning reached attack success rates from 0.9667 to 1.0000 on both datasets and all three models while often keeping clean-test performance near baseline. The results separate indiscriminate poisoning, which shows up in standard metrics, from targeted backdoor poisoning, which stays comparatively stealthy while embedding highly effective malicious behavior, and they support security-oriented evaluation beyond conventional clean-test metrics.