# Theory of Minimal Weight Perturbations in Deep Networks and its Applications for Low-Rank Activated Backdoor Attacks Source: [Theory of Minimal Weight Perturbations in Deep Networks and its Applications for Low-Rank Activated Backdoor Attacks]() Collection index: [llms.txt]() Data updated: 2026-05-20T05:00:28.635Z Authors: Bethan Evans, Jared Tanner Published: 2026-01-23T16:41:58.000Z ## Abstract The minimal norm weight perturbations of DNNs required to achieve a specified change in output are derived and the factors determining its size are discussed. These single-layer exact formulae are contrasted with more generic multi-layer Lipschitz constant based robustness guarantees; both are observed to be of the same order which indicates similar efficacy in their guarantees. These results are applied to precision-modification-activated backdoor attacks, establishing provable compression thresholds below which such attacks cannot succeed, and show empirically that low-rank compression can reliably activate latent backdoors while preserving full-precision accuracy. These expressions reveal how back-propagated margins govern layer-wise sensitivity and provide certifiable guarantees on the smallest parameter updates consistent with a desired output shift. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR10 (CA, ASR)](): Image Classification; CIFAR10; Accuracy: 93.7. - [Image Classification on Tiny ImageNet (CA, ASR)](): Image Classification; Tiny-ImageNet; Accuracy: 58.3. - [Question Answering on SQuAD (CA, ASR)](): Question Answering; SQuAD; Accuracy (CA): 76.3. ## Original sources and implementation [Original paper]() [PDF]()