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Fractional Approximation of Broad Learning System.

Shujun Wu, Jian Wang, Huaying Sun

    IEEE Transactions on Cybernetics
    |May 27, 2022
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a constructive method for designing Broad Learning Systems (BLS), ensuring approximation properties for both standard and fractional calculus applications. Numerical experiments validate the enhanced approximation capabilities of these fractional BLS models.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Fractional Calculus

    Background:

    • Broad Learning System (BLS) is a powerful neural network architecture known for its efficiency and universal approximation capabilities.
    • Existing theories prove BLS existence but lack constructive methods for network architecture and weight determination.
    • Fractional calculus offers unique properties like long-term memory and nonlocality, with potential applications in advanced modeling.

    Purpose of the Study:

    • To develop a constructive approach for determining the network structure and weights of BLS, ensuring approximation properties.
    • To extend the constructive approximation analysis of BLS to the fractional calculus domain.
    • To rigorously prove the fractional convergence behaviors of BLS.

    Main Methods:

    • Introduced two simplified BLS models by extending functions.
    • Derived an upper bound for approximation error using the modulus of continuity of Caputo fractional derivatives.
    • Provided rigorous mathematical proofs for pointwise and uniform convergence of fractional BLS.

    Main Results:

    • Established a constructive method for BLS design with guaranteed approximation properties.
    • Demonstrated the applicability of this constructive approach to fractional calculus settings.
    • Proved fractional convergence behaviors (pointwise and uniform) for the proposed BLS models.

    Conclusions:

    • The study provides a novel constructive framework for BLS, addressing limitations in existing theories.
    • The developed methods are effective for both standard and fractional approximation tasks.
    • Numerical experiments confirm the strong approximation capabilities of fractional BLS, paving the way for advanced applications.