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

Zhiyuan Ye, Xiangyu Zhou, Ji Qi, Hao Zhang, Yi Zhou · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30018 · cited by 0 works (OpenAlex) · open-access PDF

Korean

엑스그라드 (extrapolative gradient recomposition)는 CIFAR-10의 청소 입력, adversarial-input, 및 adversarial-weight-perturbed (AWP) gradients에서 업데이트를 생성하는 반대 방사선 훈련이지만, 소스 손실은 반대 방사선 상위에 업데이트의 효과를 직접적으로 특징화하지 않습니다. 우리는 ExGrad (extrapolative gradient clean control)를 소개합니다. CIFAR-10의 청소 입력, adversarial-input, 및 adversarial-weight-perturbed (AWP) gradients에서 부정적인 청소 요소가 급속하게 지배하고 방사선과 함께 규모를 증가합니다. 이 크로스 제로 개입은 광선 청소 요소를 0으로 설정하는 글로벌 솔루션이 불

Machine translation (Meta M2M100); the English original follows.

Abstract

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.

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Topics: Background subtraction, Bounded function, Subtraction, Mathematics, Affine transformation, Measure (data warehouse)

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