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

Adversarial training derives updates from surrogate losses, but source-loss descent does not directly characterize an update's effect on adversarial margins. We introduce ExGrad (extrapolative gradient recomposition), which constructs clean-input, adversarial-input, and adversarial-weight-perturbed (AWP) gradients. Virtual steps measure their margin responses, and a globally solvable three-variable problem selects coefficients over a bounded affine domain without nonnegativity constraints. Across affine radii on CIFAR-10, negative clean coefficients rapidly predominate and increase in magnitude with the radius. Cross-zero interventions show that setting the clean coefficient to zero is insufficient: mild subtraction improves PGD-20, while stronger subtraction trades clean accuracy for further PGD-20 gains. In CIFAR-10 WRN-28-4 controls, none of the three candidate-removal variants matches full ExGrad. Projection diagnostics show that negative clean coefficients usually coexist with positive net clean-axis projections, although both decrease as the radius grows. Norm-matched controls indicate that update magnitude alone does not explain the moderate-radius gains. Experiments on CIFAR-10, CIFAR-100, and ImageNet-100 show radius-dependent improvements over AWP. On CIFAR-100, ExGrad at $R=0.8$ improves all five reported metrics, including clean and AutoAttack accuracy by 3.84 and 1.75 percentage points. On ImageNet-100, the same radius improves all four robust metrics over both AWP and PGD-AT. These results identify clean-gradient subtraction as a response-revealed update preference whose strength and clean-robust operating point are controlled by the affine radius.