# Deep Adversarial Defense Against Multilevel-Lp Attacks

arXiv: https://arxiv.org/abs/2407.09251 · HTML: https://mlsanity.com/paper/2407.09251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 12 Jul 2024.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Topology and Geometry of Half-Rectified Network Optimization](https://mlsanity.com/paper/1611.01540/) (2016)
- [Adversarial Robustness Against the Union of Multiple Perturbation Models](https://mlsanity.com/paper/1909.04068/) (2019)
- [Provable robustness against all adversarial lp-perturbations for p≥ 1](https://mlsanity.com/paper/1905.11213/) (2019)
- [On Fast Adversarial Robustness Adaptation in Model-Agnostic Meta-Learning](https://mlsanity.com/paper/2102.10454/) (2021)
- [Adversarial Robustness against Multiple and Single lp-Threat Models via Quick Fine-Tuning of Robust Classifiers](https://mlsanity.com/paper/2105.12508/) (2021)
- [RAILS: A Robust Adversarial Immune-inspired Learning System](https://mlsanity.com/paper/2107.02840/) (2021)
- [ASK: Adversarial Soft k-Nearest Neighbor Attack and Defense](https://mlsanity.com/paper/2106.14300/) (2021)

## Built on by (most cited first, 1 of 1)

- [MoCo-EA: Exploiting Adversarial Mode Connectivity for Efficient Evolutionary Attacks](https://mlsanity.com/paper/2605.18919/) (2026)

## Abstract (arXiv)

Deep learning models have shown considerable vulnerability to adversarial attacks, particularly as attacker strategies become more sophisticated. While traditional adversarial training (AT) techniques offer some resilience, they often focus on defending against a single type of attack, e.g., the ℓ_∞-norm attack, which can fail for other types. This paper introduces a computationally efficient multilevel ℓp defense, called the Efficient Robust Mode Connectivity (EMRC) method, which aims to enhance a deep learning model's resilience against multiple ℓp-norm attacks. Similar to analytical continuation approaches used in continuous optimization, the method blends two p-specific adversarially optimal models, the ℓ1- and ℓ_∞-norm AT solutions, to provide good adversarial robustness for a range of p. We present experiments demonstrating that our approach performs better on various attacks as compared to AT-ℓ_∞, E-AT, and MSD, for datasets/architectures including: CIFAR-10, CIFAR-100 / PreResNet110, WideResNet, ViT-Base.