Undetectable Backdoors in Model Parameters: Hiding Sparse Secrets in High Dimensions

• URL: http://arxiv.org/abs/2605.04209v1
• Date: Tue, 05 May 2026 18:48:09 GMT
• Title: Undetectable Backdoors in Model Parameters: Hiding Sparse Secrets in High Dimensions
• Abstract summary: We present Sparse Backdoor, a supply-chain attack that plants a emphprovably undetectable backdoor in pre-trained image classifiers.<n>The attack injects a structured perturbation along a randomly chosen direction into a small subset of columns at each fully connected layer.<n>It propagates a trigger signal to an adversary-chosen target class, and masks the perturbation with an independent isotropic dither.
• Score: 27.15028670439718
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present Sparse Backdoor, a supply-chain attack that plants a \emph{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.

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