mlsanityData to 14 Oct 2026

Theory of Minimal Weight Perturbations in Deep Networks and its Applications for Low-Rank Activated Backdoor Attacks

arXiv 2601.16880 ↗First posted 23 Jan 2026cs.LG cs.IT math.ITcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 36 of its 52 references that are in the map. First posted on arXiv 23 Jan 2026.

Builds on

36 of 52 references.

References · 36

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  3. 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,372
  4. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  5. 2018MobileNetV2: Inverted Residuals and Linear Bottleneckscited by 4,795
  6. 2016SQuAD: 100,000+ Questions for Machine Comprehension of Textcited by 4,148
  7. 2015Learning both Weights and Connections for Efficient Neural Networkscited by 2,031
  8. 2017Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inferencecited by 1,593
  9. 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,417
  10. 2019Energy and Policy Considerations for Deep Learning in NLPcited by 1,254
  11. 2017Spectrally-normalized margin bounds for neural networkscited by 686
  12. 2019The State of Sparsity in Deep Neural Networkscited by 476
24 more
  1. 2016Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activationscited by 426
  2. 2014Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluationcited by 306
  3. 2018LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networkscited by 274
  4. 2016Dynamic Network Surgery for Efficient DNNscited by 233
  5. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 195
  6. 2016A guide to convolution arithmetic for deep learningcited by 185
  7. 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 161
  8. 2021Dive into Deep Learningcited by 111
  9. 2020Training robust neural networks using Lipschitz boundscited by 99
  10. 2018The Singular Values of Convolutional Layerscited by 95
  11. 2019Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networkscited by 87
  12. 2024Exploiting LLM Quantizationcited by 65
  13. 2020Methods for Pruning Deep Neural Networkscited by 49
  14. 2017Parallel Multi Channel Convolution using General Matrix Multiplicationcited by 30
  15. 2021Quantization Backdoors to Deep Learning Commercial Frameworkscited by 29
  16. 2024Small Singular Values Matter: A Random Matrix Analysis of Transformer Modelscited by 21
  17. 2016Hardware-oriented Approximation of Convolutional Neural Networkscited by 20
  18. 2021CPT: Efficient Deep Neural Network Training via Cyclic Precisioncited by 19
  19. 2021Qu-ANTI-zation: Exploiting Quantization Artifacts for Achieving Adversarial Outcomescited by 19
  20. 2021Stealthy Backdoors as Compression Artifactscited by 18
  21. 2018Rank optimality for the Burer-Monteiro factorizationcited by 12
  22. 2020Local Lipschitz Bounds of Deep Neural Networkscited by 5
  23. 2022Exact Spectral Norm Regularization for Neural Networkscited by 5
  24. 2024OutlierTune: Efficient Channel-Wise Quantization for Large Language Modelscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

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