A Geometric Probe of the Accuracy-Robustness Trade-off: Sharp Boundaries in Symmetry-Breaking Dimensional Expansion
This work addresses the fundamental accuracy-robustness trade-off problem for deep learning researchers by providing a geometric explanation, though it is incremental as it builds on existing SBDE methods.
The study investigated the trade-off between clean accuracy and adversarial robustness in deep learning using Symmetry-Breaking Dimensional Expansion (SBDE), finding that SBDE improves accuracy (e.g., from 90.47% to 95.63% on CIFAR-10) but reduces robustness due to sharp boundaries along auxiliary axes, which can be neutralized with a mask projection to restore robustness.
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 \emph{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 \emph{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.