# Parametric Noise Injection: Trainable Randomness to Improve Deep Neural Network Robustness against Adversarial Attack

arXiv: https://arxiv.org/abs/1811.09310 · HTML: https://mlsanity.com/paper/1811.09310/

## Key facts

- Cited by 123 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 22 Nov 2018.

## Built on by (most cited first, 30 of 123)

- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [HIRE-SNN: Harnessing the Inherent Robustness of Energy-Efficient Deep Spiking Neural Networks by Training with Crafted Input Noise](https://mlsanity.com/paper/2110.11417/) (2021)
- [pyvene: A Library for Understanding and Improving PyTorch Models via Interventions](https://mlsanity.com/paper/2403.07809/) (2024)
- [Random Noise Defense Against Query-Based Black-Box Attacks](https://mlsanity.com/paper/2104.11470/) (2021)
- [DeepSteal: Advanced Model Extractions Leveraging Efficient Weight Stealing in Memories](https://mlsanity.com/paper/2111.04625/) (2021)
- [Hardware-aware training for large-scale and diverse deep learning inference workloads using in-memory computing-based accelerators](https://mlsanity.com/paper/2302.08469/) (2023)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [ResSFL: A Resistance Transfer Framework for Defending Model Inversion Attack in Split Federated Learning](https://mlsanity.com/paper/2205.04007/) (2022)
- [Personality Alignment of Large Language Models](https://mlsanity.com/paper/2408.11779/) (2024)
- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [GradDiv: Adversarial Robustness of Randomized Neural Networks via Gradient Diversity Regularization](https://mlsanity.com/paper/2107.02425/) (2021)
- [Loss-Curvature Matching for Dataset Selection and Condensation](https://mlsanity.com/paper/2303.04449/) (2023)
- [Combating Adversaries with Anti-Adversaries](https://mlsanity.com/paper/2103.14347/) (2021)
- [Prompt-Matched Semantic Segmentation](https://mlsanity.com/paper/2208.10159/) (2022)
- [On the Inherent Regularization Effects of Noise Injection During Training](https://mlsanity.com/paper/2102.07379/) (2021)
- [Adversarial Attack on Attackers: Post-Process to Mitigate Black-Box Score-Based Query Attacks](https://mlsanity.com/paper/2205.12134/) (2022)
- [On the Effectiveness of Small Input Noise for Defending Against Query-based Black-Box Attacks](https://mlsanity.com/paper/2101.04829/) (2021)
- [DIFFender: Diffusion-Based Adversarial Defense against Patch Attacks](https://mlsanity.com/paper/2306.09124/) (2023)
- [Universal Spectral Adversarial Attacks for Deformable Shapes](https://mlsanity.com/paper/2104.03356/) (2021)
- [Understanding Square Loss in Training Overparametrized Neural Network Classifiers](https://mlsanity.com/paper/2112.03657/) (2021)
- [Demystifying the Adversarial Robustness of Random Transformation Defenses](https://mlsanity.com/paper/2207.03574/) (2022)
- [Fast Adversarial Training with Smooth Convergence](https://mlsanity.com/paper/2308.12857/) (2023)
- [Improving Robustness by Enhancing Weak Subnets](https://mlsanity.com/paper/2201.12765/) (2022)
- [A Simple and Yet Fairly Effective Defense for Graph Neural Networks](https://mlsanity.com/paper/2402.13987/) (2024)
- [Robust Real-World Image Super-Resolution against Adversarial Attacks](https://mlsanity.com/paper/2208.00428/) (2022)
- [Adversarial Pruning: A Survey and Benchmark of Pruning Methods for Adversarial Robustness](https://mlsanity.com/paper/2409.01249/) (2024)
- [On the robustness of randomized classifiers to adversarial examples](https://mlsanity.com/paper/2102.10875/) (2021)
- [Layer-Aware Analysis of Catastrophic Overfitting: Revealing the Pseudo-Robust Shortcut Dependency](https://mlsanity.com/paper/2405.16262/) (2024)
- [AnalogNets: ML-HW Co-Design of Noise-robust TinyML Models and Always-On Analog Compute-in-Memory Accelerator](https://mlsanity.com/paper/2111.06503/) (2021)

## Abstract (arXiv)

Recent development in the field of Deep Learning have exposed the underlying vulnerability of Deep Neural Network (DNN) against adversarial examples. In image classification, an adversarial example is a carefully modified image that is visually imperceptible to the original image but can cause DNN model to misclassify it. Training the network with Gaussian noise is an effective technique to perform model regularization, thus improving model robustness against input variation. Inspired by this classical method, we explore to utilize the regularization characteristic of noise injection to improve DNN's robustness against adversarial attack. In this work, we propose Parametric-Noise-Injection (PNI) which involves trainable Gaussian noise injection at each layer on either activation or weights through solving the min-max optimization problem, embedded with adversarial training. These parameters are trained explicitly to achieve improved robustness. To the best of our knowledge, this is the first work that uses trainable noise injection to improve network robustness against adversarial attacks, rather than manually configuring the injected noise level through cross-validation. The extensive results show that our proposed PNI technique effectively improves the robustness against a variety of powerful white-box and black-box attacks such as PGD, C & W, FGSM, transferable attack and ZOO attack. Last but not the least, PNI method improves both clean- and perturbed-data accuracy in comparison to the state-of-the-art defense methods, which outperforms current unbroken PGD defense by 1.1 % and 6.8 % on clean test data and perturbed test data respectively using Resnet-20 architecture.