This work derives a prediction-centered certificate that guarantees the stability of the smoothed model's prediction and ensures practical computability at test time and demonstrates on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, alpha-smoothing.
Abstract
Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model's prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular, we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, alpha-smoothing.
Robust multiple testing procedures for assessing equality restrictions on the coordinates of high-dimensional mean vectors are proposed. Our procedures are based on quantile-winsorization techniques, approximately control the familywise error rate (strongly) under adversarial contamination, and allow the number of hypotheses to grow exponentially with sample size, despite requiring only slightly more than two moments. Technically, our one-sample results build on recent Gaussian approximation inequalities for the distribution of high-dimensional quantile-winsorized means, whereas our two-sample results are based on extensions thereof, which we develop here and which could be of some interest in their own right.
A finite-horizon composition law for Gaussian certification from M independent coordinates, a familywise certifier protecting every coordinate and time up to T pays optimal normalized squared half-width of order log(eM) + log log(e^eT), within the sample-mean-centered rectangular class.
A consistency theory for robust neural classifiers based on the S-divergence family that requires no identifiability assumption is developed and it is proved that empirical S-divergence minimizers converge to the population-optimal equivalence class under mild regularity conditions.
Subhabrata Majumdar, Anand Deo, Partha Pratim Saha et al.· 0 citations
Adversarial training has emerged as a leading strategy for enhancing the robustness of machine learning models against adversarial attacks. Its effectiveness often wanes when faced with unseen adversarial examples, resulting in suboptimal robust generalization. To address this issue, we introduce a novel energy-based optimization strategy to improve the robust generalization by incorporating the principles of energy-based models. Our framework models the energy of natural and adversarial examples, where natural samples are assigned to lower energy and adversarial samples to higher energy. During the inference phase, the influence of adversarial perturbation can be alleviated by energy minimization. Theoretically, we show that the proposed energy-based optimization strategy yields a tighter robust-generalization bound through an explicit energy-discrepancy term; this analysis provides an explanatory bound and should not be interpreted as certified robustness. Empirically, a series of evaluations provide evidence for the efficacy of the proposed methodology under the specified threat models and evaluation protocols, showing strong and competitive performance across three extensively utilized datasets. Specifically, EM-AT achieves 77.71% standard-AA robustness on CIFAR-10 and remains highly competitive under comparable lightweight settings. The source codes are available at https://github.com/LitterQ/EM-AT.
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.