# On the Existence of Consistent Adversarial Attacks in High-Dimensional Linear Classification

arXiv: https://arxiv.org/abs/2506.12454 · HTML: https://mlsanity.com/paper/2506.12454/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 91 references that are in the map.
- First posted on arXiv 14 Jun 2025.

## Builds on (most cited first, 30 of 56)

- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [Generalisation error in learning with random features and the hidden manifold model](https://mlsanity.com/paper/2002.09339/) (2020)
- [Learning curves of generic features maps for realistic datasets with a teacher-student model](https://mlsanity.com/paper/2102.08127/) (2021)
- [Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models](https://mlsanity.com/paper/1708.03395/) (2017)
- [The Gaussian equivalence of generative models for learning with shallow neural networks](https://mlsanity.com/paper/2006.14709/) (2020)
- [More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize](https://mlsanity.com/paper/2203.06176/) (2022)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [Adversarially Robust Generalization Just Requires More Unlabeled Data](https://mlsanity.com/paper/1906.00555/) (2019)
- [Universality of empirical risk minimization](https://mlsanity.com/paper/2202.08832/) (2022)
- [A Random Matrix Analysis of Random Fourier Features: Beyond the Gaussian Kernel, a Precise Phase Transition, and the Corresponding Double Descent](https://mlsanity.com/paper/2006.05013/) (2020)
- [The role of regularization in classification of high-dimensional noisy Gaussian mixture](https://mlsanity.com/paper/2002.11544/) (2020)
- [Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions](https://mlsanity.com/paper/2106.03791/) (2021)
- [Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization](https://mlsanity.com/paper/2006.06560/) (2020)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [Precise Statistical Analysis of Classification Accuracies for Adversarial Training](https://mlsanity.com/paper/2010.11213/) (2020)
- [Adversarial Learning Guarantees for Linear Hypotheses and Neural Networks](https://mlsanity.com/paper/2004.13617/) (2020)
- [The curse of overparametrization in adversarial training: Precise analysis of robust generalization for random features regression](https://mlsanity.com/paper/2201.05149/) (2022)
- [Deterministic equivalent and error universality of deep random features learning](https://mlsanity.com/paper/2302.00401/) (2023)

## Built on by (most cited first, 2 of 2)

- [Sample-wise Adaptive Weighting for Transfer Consistency in Adversarial Distillation](https://mlsanity.com/paper/2512.10275/) (2025)
- [Explaining Machine Learning and Memorization with Statistical Mechanics](https://mlsanity.com/paper/2606.31110/) (2026)

## Abstract (arXiv)

What fundamentally distinguishes an adversarial attack from a misclassification due to limited model expressivity or finite data? In this work, we investigate this question in the setting of high-dimensional binary classification, where statistical effects due to limited data availability play a central role. We introduce a new error metric that precisely capture this distinction, quantifying model vulnerability to consistent adversarial attacks -- perturbations that preserve the ground-truth labels. Our main technical contribution is an exact and rigorous asymptotic characterization of these metrics in both well-specified models and latent space models, revealing different vulnerability patterns compared to standard robust error measures. The theoretical results demonstrate that as models become more overparameterized, their vulnerability to label-preserving perturbations grows, offering theoretical insight into the mechanisms underlying model sensitivity to adversarial attacks.