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Certified vs. Empirical Adversarial Robust-ness via Hybrid Convolutions with Attention Stochasticity
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Certified vs. Empirical Adversarial Robust-ness via Hybrid Convolutions with Attention Stochasticity

Joy Dhar, Song Xia, Manish Kumar Pandey, Maryam Haghighat, Azadeh Alavi, Ferdous Sohel, Wenyu Zhang and Nayyar Zaidi
ArXiv.org
Cornell University
2026
DOI: https://doi.org/10.48550/arxiv.2605.01519
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Open Access CC BY V4.0

Abstract

Certified Defense Empirical Defense Adversarial Robustness
We introduce Hybrid Convolutions with Attention Stochasticity (HyCAS), an adversarial defense that narrows the long-standing gap between provable robustness under L2 certificates and empirical robustness against strong L attacks, while preserving strong generalization across diverse imaging benchmarks. HyCAS unifies deterministic and randomized principles by coupling 1-Lipschitz, spectrally normalized convolutions with two stochastic components, spectral normalized random, projection filters and a randomized attention-noise mechanism, to realize a randomized defense. Injecting smoothing randomness inside the architecture yields an overall <= 2-Lipschitz network with formal certificates. Exten-sive experiments on diverse imaging benchmarks, including CIFAR-10/100, ImageNet-1k, NIH Chest X-ray, HAM10000, show that HyCAS surpasses prior leading certified and empirical defenses, boosting certified accuracy by up to 7.3% (on NIH Chest X-ray) and empirical robustness by up to 3.1% (on HAM10000), without sacrificing clean accuracy. These results show that a randomized Lipschitz constrained architecture can simultaneously improve both certified L2 and empirical L adversarial robustness, thereby supporting safer deployment of deep models in high-stakes applications. Code: https://github.com/misti1203/HyCAS

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