Statistically Undetectable Backdoors in Deep Neural Networks

Recent cryptographic results establish that neural networks can be backdoored such that no efficient algorithm can distinguish them from a clean model. These guarantees, however, have been confined to stylised architectures of limited practical relevance, leaving open whether comparable undetectability extends to modern, end-to-end trained networks. We construct such an attack mechanism for state-of-the-art architectures, closely aligned to the cryptographic notion of undetectability, by identifying backdoor channels as learned latent directions, and show that the question of undetectability reduces to a hypothesis test between two unknown distributions over model parameters, which we conjecture to be intractable in practice. The consequence of this reframing is significant: if exploitable channels within a network's latent space are statistically indistinguishable from naturally learned directions, an attacker need not introduce foreign structure but can instead exploit the geometry the network already possesses. Demonstrating the approach on ResNet and Vision Transformer architectures trained on standard image classification datasets, the attack achieves both consistently high success rates with negligible clean accuracy degradation, and resists a comprehensive suite of post-training defences, none of which neutralise the backdoor without rendering the model unusable. Our results establish that cryptographic backdoors need not be artefacts requiring exotic architectures or artificial constructions, but identifiable as latent properties inherent to the geometry of learned representations.

Deep neural networks (DNNs) remain critically vulnerable to backdoor attacks. Existing post-training detectors often require clean or surrogate data, gradients, or iterative trigger reconstruction, leading to high computational costs and limited robustness under practical model-auditing scenarios. In this paper, we propose HTell, a fast and lightweight data-free backdoor detector based on head random probing. Instead of reconstructing diverse trigger patterns, HTell inspects their unified manifestation in the prediction head: backdoored models tend to exhibit abnormal response concentration on the target class under random latent probes. HTell generates architecture-aware random latent probes, feeds them directly into the model head, and detects backdoors by analyzing class-wise response statistics, without accessing real or surrogate data, model gradients, or parameter optimization. We evaluate HTell on a large-scale benchmark containing more than 6,000 backdoored models and over 700 clean models, covering 4 datasets, 14 architectures, and 21 types of backdoor attacks. HTell achieves 99.03% true positive rate and 2.11% false positive rate with only 12.69 ms/model detection latency, reducing the time cost by over 30,000$\times$ compared with representative gradient-based detectors. These results demonstrate that head random probing provides an accurate, robust, and efficient solution for large-scale data-free backdoor model auditing.

We present Sparse Backdoor, a supply-chain attack that plants a provably undetectable backdoor in pre-trained image classifiers, including convolutional networks and Vision Transformers. The attack injects a structured sparse perturbation along a randomly chosen direction into a small subset of columns at each fully connected layer, propagating a trigger signal to an adversary-chosen target class, and masks the perturbation with an independent isotropic Gaussian dither. The dither serves a single technical purpose: it induces a clean reference distribution anchored at the pre-trained weights, against which undetectability can be formalized. Under a mild margin condition on the pre-trained classifier, we show that the dithered reference is functionally equivalent to the original classifier. We prove that distinguishing the backdoor-injected model from this reference is at least as hard as Sparse PCA detection, which is computationally infeasible under standard hardness assumptions. The guarantee holds against any probabilistic polynomial-time distinguisher with white-box access to the parameters.