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

Backdoor poisoning attacks behave counter-intuitively in high dimensions: stronger training triggers can help the defender. We study regularised generalised linear models on Gaussian-mixture data in the proportional regime ($p/n \to κ$), varying the training trigger strength $α$ against a fixed test trigger. Three phenomena emerge: (i) clean test accuracy increases with $α$; (ii) attack success peaks at a finite $α$ and then declines; and (iii) the most damaging trigger direction is the minimum eigenvector of the data covariance. We prove all three results in closed form for the squared loss, and extend (i) and (ii) to general convex GLM losses via a Gaussian-proxy fixed-point system. We identify a finite-sample noise floor proportional to $κ$ as the mechanism behind (i), invisible to classical $n \gg p$ analysis. Experiments on CIFAR-10 and Gaussian surrogates match the theory closely; ResNet-18 experiments show the same phenomena beyond the convex setting.

A Linear Approach to Data Poisoning

We investigate the theoretical foundations of data poisoning attacks in machine learning models. Our analysis reveals that the Hessian with respect to the input serves as a diagnostic tool for detecting poisoning, exhibiting spectral signatures that characterize compromised datasets. We use random matrix theory (RMT) to develop a theory for the impact of poisoning proportion and regularisation on attack efficacy in linear regression. Through QR stepwise regression, we study the spectral signatures of the Hessian in multi-output regression. We perform experiments on deep networks to show experimentally that this theory extends to modern convolutional and transformer networks under the cross-entropy loss. Based on these insights we develop preliminary algorithms to determine if a network has been poisoned and remedies which do not require further training.