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Understanding Double Descent Using VC-Theoretical Framework.

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    Deep learning networks show surprising generalization despite memorizing data. This study explains the "double descent" phenomenon using VC-theory, challenging traditional bias-variance trade-offs in machine learning.

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    Area of Science:

    • Machine Learning
    • Theoretical Computer Science
    • Statistical Learning Theory

    Background:

    • Deep learning (DL) networks are widely used, but their generalization capabilities are not fully understood theoretically.
    • Conventional statistical learning theory suggests a bias-variance trade-off, where model complexity is balanced to avoid underfitting and overfitting.

    Purpose of the Study:

    • To provide a theoretical explanation for the generalization performance of DL networks, particularly the
    • double descent
    • phenomenon.
    • To analyze why overparameterized networks can generalize well even when memorizing training data.

    Main Methods:

    • Utilizing the VC-theoretical framework to analyze generalization performance in classification settings.
    • Developing a VC-theoretical explanation for the
    • double descent
    • phenomenon.
    • Empirically modeling double descent curves using analytic VC-bounds for various learning methods.

    Main Results:

    • A VC-theoretical explanation for the
    • double descent
    • phenomenon in DL networks is presented.
    • Empirical validation of the theoretical findings using support vector machines (SVM), least squares (LS), and multilayer perceptron classifiers.
    • Demonstrated that overparameterized models can achieve good generalization.

    Conclusions:

    • The VC-theoretical framework offers insights into the generalization of overparameterized DL networks.
    • The study challenges conventional views on model complexity and the bias-variance trade-off.
    • The findings contribute to a better understanding of learning mechanisms in complex models.