# Purification Of Contaminated Convolutional Neural Networks Via Robust Recovery: An Approach with Theoretical Guarantee in One-Hidden-Layer Case

arXiv: https://arxiv.org/abs/2407.11031 · HTML: https://mlsanity.com/paper/2407.11031/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Backdoor and data poisoning attacks, one of 12 directions in LLM safety and security.
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Placed in

- LLM safety and security / [Backdoor and data poisoning attacks](https://mlsanity.com/safety/backdoor-and-data-poisoning-attacks/)

## Builds on (most cited first, 17 of 17)

- [Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning](https://mlsanity.com/paper/1712.05526/) (2017)
- [Hidden Trigger Backdoor Attacks](https://mlsanity.com/paper/1910.00033/) (2019)
- [Modifying Memories in Transformer Models](https://mlsanity.com/paper/2012.00363/) (2020)
- [Practical Detection of Trojan Neural Networks: Data-Limited and Data-Free Cases](https://mlsanity.com/paper/2007.15802/) (2020)
- [Handcrafted Backdoors in Deep Neural Networks](https://mlsanity.com/paper/2106.04690/) (2021)
- [P-CNN: Pose-based CNN Features for Action Recognition](https://mlsanity.com/paper/1506.03607/) (2015)
- [Causality-based Neural Network Repair](https://mlsanity.com/paper/2204.09274/) (2022)
- [Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimator](https://mlsanity.com/paper/1904.06288/) (2019)
- [Adaptive Hard Thresholding for Near-optimal Consistent Robust Regression](https://mlsanity.com/paper/1903.08192/) (2019)
- [Transform Quantization for CNN (Convolutional Neural Network) Compression](https://mlsanity.com/paper/2009.01174/) (2020)
- [Learning Non-overlapping Convolutional Neural Networks with Multiple Kernels](https://mlsanity.com/paper/1711.03440/) (2017)
- [Backdoor Secrets Unveiled: Identifying Backdoor Data with Optimized Scaled Prediction Consistency](https://mlsanity.com/paper/2403.10717/) (2024)
- [PSBD: Prediction Shift Uncertainty Unlocks Backdoor Detection](https://mlsanity.com/paper/2406.05826/) (2024)
- [Denoising Noisy Neural Networks: A Bayesian Approach with Compensation](https://mlsanity.com/paper/2105.10699/) (2021)
- [Towards Understanding How Self-training Tolerates Data Backdoor Poisoning](https://mlsanity.com/paper/2301.08751/) (2023)
- [Model Repair: Robust Recovery of Over-Parameterized Statistical Models](https://mlsanity.com/paper/2005.09912/) (2020)
- [Tensor Recovery from Noisy and Multi-Level Quantized Measurements](https://mlsanity.com/paper/1912.02588/) (2019)

## Abstract (arXiv)

Convolutional neural networks (CNNs), one of the key architectures of deep learning models, have achieved superior performance on many machine learning tasks such as image classification, video recognition, and power systems. Despite their success, CNNs can be easily contaminated by natural noises and artificially injected noises such as backdoor attacks. In this paper, we propose a robust recovery method to remove the noise from the potentially contaminated CNNs and provide an exact recovery guarantee on one-hidden-layer non-overlapping CNNs with the rectified linear unit (ReLU) activation function. Our theoretical results show that both CNNs' weights and biases can be exactly recovered under the overparameterization setting with some mild assumptions. The experimental results demonstrate the correctness of the proofs and the effectiveness of the method in both the synthetic environment and the practical neural network setting. Our results also indicate that the proposed method can be extended to multiple-layer CNNs and potentially serve as a defense strategy against backdoor attacks.