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AMITE: A Novel Polynomial Expansion for Analyzing Neural Network Nonlinearities.

Mauro J Sanchirico, Xun Jiao, C Nataraj

    IEEE Transactions on Neural Networks and Learning Systems
    |December 14, 2021
    PubMed
    Summary
    This summary is machine-generated.

    A new method, analytically modified integral transform expansion (AMITE), consistently provides six desired properties for analyzing neural network nonlinearities, unlike previous approaches. This enables more robust verification, explainability, and security for neural networks.

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    Area of Science:

    • * Artificial Intelligence
    • * Computational Mathematics

    Background:

    • * Polynomial expansions are crucial for analyzing neural network nonlinearities, aiding verification, explainability, and security.
    • * Existing methods like Taylor and Chebyshev expansions have limitations, lacking a consistent approach to combine desirable properties.
    • * There's a need for a unified expansion method offering properties such as exact error formulas and adjustable domains.

    Purpose of the Study:

    • * To introduce a novel expansion technique, analytically modified integral transform expansion (AMITE), for neural network analysis.
    • * To address the limitations of existing methods by providing a consistent expansion with multiple desired properties.
    • * To demonstrate the applicability and effectiveness of AMITE in analyzing neural network nonlinearities.

    Main Methods:

    • * Development of AMITE, an integral transform expansion modified with convergence criteria.
    • * Application of AMITE to hyperbolic tangent and rectified linear unit activation functions.
    • * Comparison of AMITE with classical Chebyshev, Taylor, and numerical expansion methods.

    Main Results:

    • * AMITE is the first method to consistently provide six previously mutually exclusive expansion properties.
    • * AMITE yields exact formulas for coefficients and exact expansion errors.
    • * Demonstrated effectiveness in extracting polynomial forms from black-box MLPs and range bounding FFNNs.

    Conclusions:

    • * AMITE offers a significant advancement in analyzing and approximating neural network nonlinearities.
    • * The method enhances theoretical analysis and systematic testing of neural networks.
    • * AMITE opens new avenues for research in AI verification, explainability, and security.