# Cert-SSBD: Certified Backdoor Defense with Sample-Specific Smoothing Noises

arXiv: https://arxiv.org/abs/2504.21730 · HTML: https://mlsanity.com/paper/2504.21730/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 80 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning](https://mlsanity.com/paper/1712.05526/) (2017)
- [Fine-Pruning: Defending Against Backdooring Attacks on Deep Neural Networks](https://mlsanity.com/paper/1805.12185/) (2018)
- [Backdoor Learning: A Survey](https://mlsanity.com/paper/2007.08745/) (2020)
- [Invisible Backdoor Attack with Sample-Specific Triggers](https://mlsanity.com/paper/2012.03816/) (2020)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Attack of the Tails: Yes, You Really Can Backdoor Federated Learning](https://mlsanity.com/paper/2007.05084/) (2020)
- [Anti-Backdoor Learning: Training Clean Models on Poisoned Data](https://mlsanity.com/paper/2110.11571/) (2021)
- [A new Backdoor Attack in CNNs by training set corruption without label poisoning](https://mlsanity.com/paper/1902.11237/) (2019)
- [Detecting AI Trojans Using Meta Neural Analysis](https://mlsanity.com/paper/1910.03137/) (2019)
- [SentiNet: Detecting Localized Universal Attacks Against Deep Learning Systems](https://mlsanity.com/paper/1812.00292/) (2018)
- [Stronger Data Poisoning Attacks Break Data Sanitization Defenses](https://mlsanity.com/paper/1811.00741/) (2018)
- [SPECTRE: Defending Against Backdoor Attacks Using Robust Statistics](https://mlsanity.com/paper/2104.11315/) (2021)
- [Adversarial Machine Learning -- Industry Perspectives](https://mlsanity.com/paper/2002.05646/) (2020)
- [RAB: Provable Robustness Against Backdoor Attacks](https://mlsanity.com/paper/2003.08904/) (2020)
- [Deep Partition Aggregation: Provable Defense against General Poisoning Attacks](https://mlsanity.com/paper/2006.14768/) (2020)
- [MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radius](https://mlsanity.com/paper/2001.02378/) (2020)
- [An Embarrassingly Simple Approach for Trojan Attack in Deep Neural Networks](https://mlsanity.com/paper/2006.08131/) (2020)
- [Intrinsic Certified Robustness of Bagging against Data Poisoning Attacks](https://mlsanity.com/paper/2008.04495/) (2020)
- [On Certifying Robustness against Backdoor Attacks via Randomized Smoothing](https://mlsanity.com/paper/2002.11750/) (2020)
- [Black-box Dataset Ownership Verification via Backdoor Watermarking](https://mlsanity.com/paper/2209.06015/) (2022)
- [Certified Robustness of Nearest Neighbors against Data Poisoning and Backdoor Attacks](https://mlsanity.com/paper/2012.03765/) (2020)
- [Domain Watermark: Effective and Harmless Dataset Copyright Protection is Closed at Hand](https://mlsanity.com/paper/2310.14942/) (2023)
- [Improved Certified Defenses against Data Poisoning with (Deterministic) Finite Aggregation](https://mlsanity.com/paper/2202.02628/) (2022)
- [Explanation as a Watermark: Towards Harmless and Multi-bit Model Ownership Verification via Watermarking Feature Attribution](https://mlsanity.com/paper/2405.04825/) (2024)
- [IBD-PSC: Input-level Backdoor Detection via Parameter-oriented Scaling Consistency](https://mlsanity.com/paper/2405.09786/) (2024)
- [Few-Shot Backdoor Attacks on Visual Object Tracking](https://mlsanity.com/paper/2201.13178/) (2022)
- [Towards Stealthy Backdoor Attacks against Speech Recognition via Elements of Sound](https://mlsanity.com/paper/2307.08208/) (2023)

## Built on by (most cited first, 4 of 4)

- [Cert-LAS: Toward Certified Model Ownership Verification for Text-to-Image Diffusion Models via Layer-Adaptive Smoothing](https://mlsanity.com/paper/2605.29809/) (2026)
- [Provable Robustness against Backdoor Attacks via the Primal-Dual Perspective on Differential Privacy](https://mlsanity.com/paper/2605.21780/) (2026)
- [TimeGuard: Channel-wise Pool Training for Backdoor Defense in Time Series Forecasting](https://mlsanity.com/paper/2605.22365/) (2026)
- [A Comprehensive Review of One-Pixel Attack: Research Status, Taxonomy, Applications, Regulation Policy and Future Directions](https://mlsanity.com/paper/2610.00125/) (2026)

## Abstract (arXiv)

Deep neural networks (DNNs) are vulnerable to backdoor attacks, where an attacker manipulates a small portion of the training data to implant hidden backdoors into the model. The compromised model behaves normally on clean samples but misclassifies backdoored samples into the attacker-specified target class, posing a significant threat to real-world DNN applications. Currently, several empirical defense methods have been proposed to mitigate backdoor attacks, but they are often bypassed by more advanced backdoor techniques. In contrast, certified defenses based on randomized smoothing have shown promise by adding random noise to training and testing samples to counteract backdoor attacks. In this paper, we reveal that existing randomized smoothing defenses implicitly assume that all samples are equidistant from the decision boundary. However, it may not hold in practice, leading to suboptimal certification performance. To address this issue, we propose a sample-specific certified backdoor defense method, termed Cert-SSB. Cert-SSB first employs stochastic gradient ascent to optimize the noise magnitude for each sample, ensuring a sample-specific noise level that is then applied to multiple poisoned training sets to retrain several smoothed models. After that, Cert-SSB aggregates the predictions of multiple smoothed models to generate the final robust prediction. In particular, in this case, existing certification methods become inapplicable since the optimized noise varies across different samples. To conquer this challenge, we introduce a storage-update-based certification method, which dynamically adjusts each sample's certification region to improve certification performance. We conduct extensive experiments on multiple benchmark datasets, demonstrating the effectiveness of our proposed method. Our code is available at https://github.com/NcepuQiaoTing/Cert-SSB.