Xingyu Zhao

Deep learning models are notoriously vulnerable to imperceptible perturbations. Most existing research centers on adversarial robustness (AR), which evaluates models under worst-case scenarios by examining the existence of deterministic adversarial examples (AEs). In contrast, probabilistic robustness (PR) adopts a statistical perspective, measuring the probability that predictions remain correct under stochastic perturbations. While PR is widely regarded as a practical complement to AR, dedicated training methods for improving PR are still relatively underexplored, albeit with emerging progress. Among the few PR-targeted training methods, we identify three limitations: i non-comparable evaluation protocols; ii limited comparisons to strong AT baselines despite anecdotal PR gains from AT; and iii no unified framework to compare the generalization of these methods. Thus, we introduce PRBench, the first benchmark dedicated to evaluating improvements in PR achieved by different robustness training methods. PRBench empirically compares most common AT and PR-targeted training methods using a comprehensive set of metrics, including clean accuracy, PR and AR performance, training efficiency, and generalization error (GE). We also provide theoretical analysis on the GE of PR performance across different training methods. Main findings revealed by PRBench include: AT methods are more versatile than PR-targeted training methods in terms of improving both AR and PR performance across diverse hyperparameter settings, while PR-targeted training methods consistently yield lower GE and higher clean accuracy. A leaderboard comprising 222 trained models across 7 datasets and 10 model architectures is publicly available at https://tmpspace.github.io/PRBenchLeaderboard/.

Deep learning (DL) models, despite their remarkable success, remain vulnerable to small input perturbations that can cause erroneous outputs, motivating the recent proposal of probabilistic robustness (PR) as a complementary alternative to adversarial robustness (AR). However, existing PR formulations assume a fixed and known perturbation distribution, an unrealistic expectation in practice. To address this limitation, we propose non-parametric probabilistic robustness (NPPR), a more practical PR metric that does not rely on any predefined perturbation distribution. Following the non-parametric paradigm in statistical modeling, NPPR learns an optimized perturbation distribution directly from data, enabling conservative PR evaluation under distributional uncertainty. We further develop an NPPR estimator based on a Gaussian Mixture Model (GMM) with Multilayer Perceptron (MLP) heads and bicubic up-sampling, covering various input-dependent and input-independent perturbation scenarios. Theoretical analyses establish the relationships among AR, PR, and NPPR. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny ImageNet across ResNet18/50, WideResNet50 and VGG16 validate NPPR as a more practical robustness metric, showing up to 40\% more conservative (lower) PR estimates compared to assuming those common perturbation distributions used in state-of-the-arts.