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On the Minimal Adversarial Perturbation for Deep Neural Networks With Provable Estimation Error.

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    This study introduces novel methods to quantify Deep Neural Network robustness against adversarial perturbations. The proposed strategies accurately estimate the minimal adversarial perturbation, offering provable guarantees for network security.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Computer Vision

    Background:

    • Deep Neural Networks (DNNs) excel in perception and control but face trustworthiness issues.
    • Adversarial perturbations pose a significant threat, necessitating robust quantification techniques.
    • Euclidean distance to the classification boundary is a key metric for input robustness, but hard to compute for DNNs.

    Purpose of the Study:

    • To propose lightweight strategies for estimating the minimal adversarial perturbation in DNNs.
    • To develop a theory for error estimation of approximate distances compared to theoretical ones.
    • To provide provable robustness guarantees against adversarial attacks.

    Main Methods:

    • Developed two novel, lightweight algorithms to approximate the minimal adversarial perturbation.
    • Formulated an error estimation theory to bound the approximation error.
    • Conducted extensive experiments to validate the algorithms and theoretical findings.

    Main Results:

    • The proposed strategies effectively approximate the theoretical distance for inputs near the classification boundary.
    • The methods provide provable robustness guarantees against adversarial perturbations.
    • Experimental results support the theoretical findings on error estimation and approximation.

    Conclusions:

    • The novel strategies offer a practical solution for assessing DNN robustness.
    • This work advances the field of provable defenses against adversarial attacks.
    • The findings contribute to building more trustworthy and secure AI systems.