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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
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Sparse-PGD: A Unified Framework for Sparse Adversarial Perturbations Generation.

Xuyang Zhong, Chen Liu

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |November 7, 2025
    PubMed
    Summary

    This study introduces Sparse-PGD, an efficient method for creating sparse adversarial perturbations. Models trained with this technique show state-of-the-art robustness against these attacks.

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    Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Adversarial perturbations pose a significant threat to machine learning model security.
    • Evaluating model robustness against sparse perturbations (unstructured and structured) is crucial.

    Purpose of the Study:

    • To develop an effective and efficient framework for generating sparse adversarial perturbations.
    • To comprehensively evaluate model robustness against these perturbations.
    • To enhance model robustness through adversarial training.

    Main Methods:

    • Proposed a white-box Projected Gradient Descent (PGD)-like attack method named Sparse-PGD.
    • Combined Sparse-PGD with a black-box attack for comprehensive robustness evaluation.
    • Utilized Sparse-PGD for adversarial training to build robust models.

    Main Results:

    • Sparse-PGD demonstrated strong performance in generating sparse adversarial perturbations across various scenarios.
    • The combined attack approach provided reliable evaluation of model robustness.
    • Adversarial training using Sparse-PGD significantly improved model resilience.

    Conclusions:

    • Sparse-PGD is an effective and efficient tool for generating sparse adversarial perturbations.
    • Adversarial training with Sparse-PGD yields state-of-the-art robustness against sparse attacks.
    • The proposed framework offers a reliable method for assessing and enhancing model security.