Provable Adversarial Detection: Prime Quantization meets Gromov--Wasserstein

Vision-language pre-trained models (VLPs) are widely used in real-world applications. However, they remain vulnerable to adversarial attacks. Although adversarial detection methods have demonstrated success in single-modality settings (either vision or language), their effectiveness and reliability in multimodal models such as VLPs remain largely unexplored. In this work, we study the geometry of VLP embedding spaces and observe structured anisotropy that differs from unimodal vision models. Our theoretical analysis shows that under this anisotropic structure, adversarial attacks increase the expected geometric separation between clean and adversarial examples (AEs). Specifically, we demonstrate that AEs consistently exhibit greater expected distances to randomly sampled points than their clean counterparts, indicating that AEs tend to push representations out of manifold regions. Building on these insights, we propose GeoDetect, which leverages these off-manifold deviations via geometric scores to identify AEs. Through comprehensive evaluations, we show that our approach reliably detects AEs across diverse VLP architectures and threat settings, covering unimodal and multimodal attacks as well as adaptive attacks, thereby providing a robust and practical approach to improving the safety and reliability of these models.

Deep classifiers deployed in safety-critical services like autonomous-driving perception remain vulnerable to small adversarial perturbations. Certified $\ell_2$ defenses today face a costly trade-off: randomized smoothing (RS) requires hundreds of noisy queries per input, while Lipschitz networks (LN) constrain the architecture and sacrifice clean accuracy. We take a detection-oriented approach instead: rather than certifying that predictions are invariant inside an $\ell_2$ ball, we certify that adversarial inputs within an $\ell_2$ ball are detected --- a guarantee aligned with security-critical deployments where missing an attack is costlier than flagging a clean input. To realize this, we prove a Lipschitz-margin reduction from certified $\ell_2$ robustness to certified detection, which reduces the problem to handling a single Lipschitz constant $L$. We introduce two detector families: $\mathbb{D}_{Adv}$, which estimates $L$ from a single defender-side perturbed pair, and $\mathbb{D}_{lc}$, which augments that pair with a local margin centroid to keep the estimate above what the certificate requires. Both deploy on any pretrained classifier without retraining. With a valid global bound, the detector is fully certified at that radius; with a local estimate $L'$, certification is sample-wise and applies only when our certified condition holds. Across MNIST, CIFAR-10, and ImageNet-1k on four backbones (LeNet-5, VGG16, ResNet-50, ViT-B/16), our detectors match or outperform five baselines (CTT, SortNet, CRM, ContraNet, A$^2$D). For CIFAR-10 with 1-Lipschitz SortNet, our reduction delivers $100\%$ certified detection at the lowest FPR among compared certified detectors; on the standard CIFAR-10 VGG16, our detectors reject all evaluated in-budget adversarial examples, with 62-82% both rejected and formally certified.

The nonuniform and growing impact of adversarial noise across the layers of deep neural networks has been used in the literature, without a formal mathematical justification, to detect adversarial inputs and improve robustness. In this work, we study this phenomenon in detail and present a formal adversarial noise amplification theorem. We specify a set of sufficient conditions under which the adversarial noise amplification is mathematically guaranteed. Based on theoretical observations, we propose a novel training methodology with a custom spectral loss function and a specific architectural design to enhance the amplification signal for detecting adversarial data. Finally, we introduce a new, lightweight detection mechanism that leverages the enhanced amplification signal and operates entirely at inference time. To validate our approach, we demonstrate the detector's efficacy against both state-of-the-art attacks and a purpose-built adaptive attack, confirming that enhanced amplification can serve as a robust and reliable signal for adversarial defense.