# A Geometric Probe of the Accuracy-Robustness Trade-off: Sharp Boundaries in Symmetry-Breaking Dimensional Expansion

arXiv: https://arxiv.org/abs/2602.17948 · HTML: https://mlsanity.com/paper/2602.17948/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [On the uncertainty principle of neural networks](https://mlsanity.com/paper/2205.01493/) (2022)
- [Quantum-Inspired Analysis of Neural Network Vulnerabilities: The Role of Conjugate Variables in System Attacks](https://mlsanity.com/paper/2402.10983/) (2024)
- [Symmetry Breaking in Neural Network Optimization: Insights from Input Dimension Expansion](https://mlsanity.com/paper/2409.06402/) (2024)

## Abstract (arXiv)

The trade-off between clean accuracy and adversarial robustness is a pervasive phenomenon in deep learning, yet its geometric origin remains elusive. In this work, we utilize Symmetry-Breaking Dimensional Expansion (SBDE) as a controlled probe to investigate the mechanism underlying this trade-off. SBDE expands input images by inserting constant-valued pixels, which breaks translational symmetry and consistently improves clean accuracy (e.g., from 90.47% to 95.63% on CIFAR-10 with ResNet-18) by reducing parameter degeneracy. However, this accuracy gain comes at the cost of reduced robustness against iterative white-box attacks. By employing a test-time mask projection that resets the inserted auxiliary pixels to their training values, we demonstrate that the vulnerability stems almost entirely from the inserted dimensions. The projection effectively neutralizes the attacks and restores robustness, revealing that the model achieves high accuracy by creating sharp boundaries (steep loss gradients) specifically along the auxiliary axes. Our findings provide a concrete geometric explanation for the accuracy-robustness paradox: the optimization landscape deepens the basin of attraction to improve accuracy but inevitably erects steep walls along the auxiliary degrees of freedom, creating a fragile sensitivity to off-manifold perturbations.