ExGrad: Beyond Suppression - Explicit Clean-Gradient Subtraction in Adversarial Training

Adversarial training remains one of the most effective defenses against adversarial attacks, but its standard PGD-based training is computationally expensive because adversarial examples are generated for every training sample. Selective adversarial training reduces this cost by perturbing only a subset of samples. However, existing selective techniques typically rely on point-wise difficulty signals such as loss, entropy, margin, or gradients. We show that these point-wise criteria do not capture local instability in a sample's neighborhood. Motivated by this, we propose Augmentation-Guided Adversarial Training (AGAT), a selective adversarial training framework that uses augmentation-induced local variation to allocate samples with unstable neighborhoods for adversarial training. AGAT ranks samples using Augmentation-based Local Stability (ALS), a lightweight score that measures the normalized change in model logits between an input and its label-preserving augmented variant. Experiments across different architectures on MNIST, CIFAR-10, CIFAR-100, and Tiny-ImageNet-200 demonstrate that AGAT achieves comparable or higher robust accuracy while applying adversarial supervision to only 20-30% of the training samples in each minibatch. AGAT also requires less training time than all other adversarial training baselines in the computational cost evaluation.

Generating adversarial examples at scale is a core primitive for robustness evaluation, adversarial training, and red-teaming, yet even "fast" attacks such as FGSM remain throughput-limited by the cost of a backward pass. We introduce a family of attacks that eliminates the backward pass by predicting the input gradient from forward-pass hidden states via a lightweight linear regression. Theoretically, we derive exact affine conditional gradient means, showing optimality in the (idealized) NTK regime. Empirically, our methods work when applied to practical finite-width models; we recover much of FGSM's attack performance while using only a small fraction of the time, corresponding to a $532\%$ increase in throughput. These results suggest gradient prediction as a simple and general route to significantly faster adversarial generation under realistic wall-clock constraints.

This work concerns adversarial training against the small-norm adversarial examples that arise from the inherent input instability of a trained deep neural network. Examples in this class are small as measured in the relative $\ell^2$-norm, and therefore lie in the neighborhood of the input on which the model acts approximately linearly, the regime in which the perturbation remains imperceptible. We first show that such examples can be computed directly from the trained network parameters, without input gradient iterations, by means of a linearization called the low-rank Householder expansion (LRHE). The expansion describes the composed affine map rather than any individual layer, and the directions it identifies are read from the activation pattern already available in the forward pass. We then propose a simple adversarial training scheme built on this construction. No differentiation with respect to the input is performed at any point: training requires only additional forward evaluations, with weight parameters updated by the standard backward pass, and the inner maximization of the usual min-max formulation is eliminated entirely. That such a regularizer exists is our main finding: the methods that dispense with the inner search all obtain their local geometry by differentiating with respect to the input, and we show this is not necessary. The regularizer costs the equivalent of $2.8$ PGD steps per epoch, an $8.7\times$ reduction relative to 40-step adversarial training on MNIST and below the cost of 3-step training. The resulting models match three-step PGD adversarial training for relative $\ell^2$ budgets $\varepsilon \le 0.02$ and 40-step training for $\varepsilon \le 0.012$, falling away beyond, consistent with the locality of the expansion.