# The Uncanny Valley: Exploring Adversarial Robustness from a Flatness Perspective

arXiv: https://arxiv.org/abs/2405.16918 · HTML: https://mlsanity.com/paper/2405.16918/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 70 references that are in the map.
- First posted on arXiv 27 May 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Adversarial Patch](https://mlsanity.com/paper/1712.09665/) (2017)
- [BERT-ATTACK: Adversarial Attack Against BERT Using BERT](https://mlsanity.com/paper/2004.09984/) (2020)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)

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

- [Flatness is Necessary, Neural Collapse is Not: Rethinking Generalization via Grokking](https://mlsanity.com/paper/2509.17738/) (2025)
- [Hide & Seek: Transformer Symmetries Obscure Sharpness & Riemannian Geometry Finds It](https://mlsanity.com/paper/2505.05409/) (2025)
- [An accurate flatness measure to estimate the generalization performance of CNN models](https://mlsanity.com/paper/2603.09016/) (2026)
- [Generalization in Neural Networks Through the Lens of Magnitude Potential](https://mlsanity.com/paper/2610.01633/) (2026)

## Abstract (arXiv)

Flatness of the loss surface not only correlates positively with generalization, but is also related to adversarial robustness since perturbations of inputs relate non-linearly to perturbations of weights. In this paper, we empirically analyze the relation between adversarial examples and relative flatness with respect to the parameters of one layer. We observe a peculiar property of adversarial examples in the context of relative flatness: during an iterative first-order white-box attack, the flatness of the loss surface measured around the adversarial example first becomes sharper until the label is flipped, but if we keep the attack running, it runs into a flat uncanny valley where the label remains flipped. In extensive experiments, we observe this phenomenon across various model architectures and datasets, even for adversarially trained models. Our results also extend to large language models (LLMs), but due to the discrete nature of the input space and comparatively weak attacks, adversarial examples rarely reach truly flat regions. Most importantly, this phenomenon shows that flatness alone cannot explain adversarial robustness unless we can also guarantee the behavior of the function around the examples. We, therefore theoretically connect relative flatness to adversarial robustness by bounding the third derivative of the loss surface, underlining the need for flatness in combination with a low global Lipschitz constant for a robust model.