Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms

Deep neural networks are vulnerable to adversarial perturbations that can simultaneously degrade prediction robustness and individual fairness across diverse application settings. However, existing evaluation protocols typically assess these dimensions in isolation, thereby obscuring critical failure modes. To bridge this gap, we formalize Robust Individual Fairness (RIF): under semantic-preserving (truth-condition-preserving) perturbations, predictions should remain both correct with respect to the ground truth and invariant across semantically equivalent individuals. To surface RIF violations in practice, we introduce RIFair, a black-box adversarial framework that leverages a decoupled perturbation strategy to construct semantically preserved yet unrobust and/or unfair instance pairs. Experiments across multiple model architectures and real-world textual datasets show that robustness-only or fairness-only metrics often miss Robust Biased and Unrobust Fair behaviors. RIFair}reliably exposes these hidden vulnerabilities, supporting RIF as a necessary criterion for trustworthy model assessment. The experimental code is publicly available at https://github.com/Xuran-LI/RIFair.

Adversarial robustness is commonly evaluated with predefined attack ensembles, such as AutoAttack, at a single perturbation budget $\varepsilon$ and on a selective choice of perturbation norms. We argue this formulation is fundamentally limited. First, robustness--perturbation curves may intersect or decay at different rates across models, making single-$\varepsilon$ rankings unstable. Second, current ensembles provide no evidence of optimality, leaving an unknown gap to worst-case performance. Third, fixed attack configurations provide no systematic control over the trade-off between attack strength and evaluation cost. To address these limitations, we introduce a unified evaluation framework based on a comprehensive pool of minimum-norm attacks and robustness--perturbation curves across $\ell_0$, $\ell_1$, $\ell_2$ and $\ell_\infty$ norms. We define the attack frontier as the worst-case robustness estimate the attack pool produces against a model. We then formalize evaluation as a frontier-approximation problem, constructing minimum-norm attack ensembles, optimized subsets of the comprehensive pool, that approach the frontier under a controllable query budget, with larger budgets monotonically tightening the estimate. Furthermore, we define the defense frontier as the maximum robustness across the model set at each perturbation size. We finally propose the Defense Optimality Index to rank defenses by their gap to the defense frontier, providing a ranking without selecting a reference $\varepsilon$. On CIFAR-10 and ImageNet, our ensembles match or exceed AutoAttack on most defenses at every budget tier, at fixed and controllable query cost, offering practitioners a query-controlled, curve-based alternative to fixed-$\varepsilon$ evaluation.

Adversarial robustness research has produced hundreds of defended models over the past decade, yet the literature almost universally reports robustness results in isolation: standard (clean) accuracy and adversarial accuracy of the robust model are shown, but the gap to the corresponding vanilla model is rarely quantified. We introduce VanillaBench, a systematic benchmark that makes this gap explicit. For every adversarially-trained model catalogued by RobustBench across four threat models, we compute the accuracy difference against multiple vanilla references from Papers with Code, computed over both all entries and no-extra-data entries, the best vanilla model as of the robust model's publication year, and an architecture-matched baseline. Across all 186 robust models, the mean delta clean relative to the best vanilla model ranges from -7.7 to -29.5 percentage points, and even the single most robust model per track still trails its temporal vanilla counterpart by 4.0-21.0 points. The architecture-matched comparison, which isolates the effect of adversarial training from architectural differences, reveals a mean gap of -3.5 to -17.5 points. Restricting this architecture-matched comparison to models whose vanilla accuracy is known for the exact same architecture, rather than approximated from a related one, narrows the gap to -4.0 to -14.0 points. These results demonstrate that the robustness-accuracy trade-off is substantially larger than what is typically conveyed by individual papers. This information is critical for practitioners and decision-makers. When deploying models in real-world settings, the accuracy cost of robustness directly affects business outcomes, yet current publications do not provide the vanilla baseline needed to assess it. We argue that future robustness evaluations should report vanilla-referenced accuracy gaps as a standard component.