A Few Large Shifts: Layer-Inconsistency Based Minimal Overhead Adversarial Example Detection

Adversarial attacks fool deep image classifiers by adding tiny, almost invisible noise patterns to a clean image. The standard $\ell^\infty$-bounded attacks (FGSM and PGD) produce high-frequency, near-random sign patterns at the pixel level: small in $\ell^2$, but carrying disproportionate gradient energy. We exploit this with a single-shot, training-free detector using the high-order Corbino-Castillo mimetic operators from the open-source MOLE library. No retraining, no surrogate classifier, no access to the network under attack: the verdict is a property of the input alone, computed in $O(HW)$ time. We illustrate the detector on the standard "peppers" test image: untargeted FGSM and PGD attacks at the $\ell^\infty$ budget $\varepsilon = 16/255$ flip SqueezeNet's prediction from "bell pepper" to "doormat" (FGSM) and "maraca" (PGD), and the detector separates these adversarial inputs from the clean image by $4.1\times$-$5.0\times$ (FGSM) and $1.9\times$-$2.2\times$ (PGD). The margin grows monotonically with the operator order $k$, while an equal-amplitude smooth perturbation leaves the statistic within 1% of its clean value.

Almost all adversarial attacks add an imperceptible perturbation to fool a model. We instead study the opposite: a large, clearly visible perturbation that causes the model to keep its original, correct prediction, even though a human would no longer recognize the image. Prior work showed such examples can be generated at scale but left three questions untested: whether humans really perform worse than the model, whether standard out-of-distribution (OOD) detection and calibration tools catch it, and whether existing defenses mitigate it. We answer all three on MNIST, CIFAR-10, and ImageNet. (i) An independent recognizer proxy drops to ~49% on CIFAR-10 while the model stays at 100% -- a gap a small human pilot (N=5) corroborates directly and that is not explained by signal loss (a matched-magnitude Gaussian control degrades recognizability faster); a CLIP zero-shot proxy confirms the gap at ImageNet scale too. (ii) Confidence- and energy-based OOD detectors and calibration are structurally blind (0% detection, ECE ~= 0), while a feature-space Mahalanobis detector flags 100% -- but is evaded by an adaptive attacker at no cost to success. (iii) No classical defense, including adversarial training (45% robust accuracy), reduces attack success (correlation with large-epsilon_l resistance r ~= 0). A mechanistic analysis further shows the attack destroys low-level texture far faster than edge/shape structure.

Deep neural networks process data through a cascade of representations: input features, hidden activations, logits, and loss. While perturbations at the input, logit, and label levels have been systematically studied, the intermediate hidden activations, which constitute the bulk of the network's computation, have received no unified perturbation analysis. In this paper, we establish a unified framework for hidden activation perturbation, revealing that Dropout, Manifold Mixup, adversarial feature perturbation, and related methods all impose specific forms of activation perturbation but with class-agnostic or random strategies. We conjecture that expansive perturbation (increasing activation norm) acts as positive augmentation, while contractive perturbation (decreasing activation norm) acts as negative augmentation, and that the perturbation layer determines whether the effect resembles input-level augmentation (shallow layers) or logit-level manipulation (deep layers). We propose Learning to Perturb Activations (LPA), which adaptively perturbs activations at a selected hidden layer with class-level perturbations learned via PGD. We further provide theoretical analysis connecting activation perturbation to flat minima and perturbation amplification through layers. Experiments on balanced classification, long-tail classification, and domain generalization demonstrate that LPA consistently outperforms existing methods and provides complementary benefits to logit perturbation methods such as LPL.