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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Signal Processing

    Background:

    • Understanding the internal workings of fully connected neural networks is crucial for interpretability.
    • Current methods often lack a clear link between network parameters and functional behavior.

    Purpose of the Study:

    • To investigate the spectral properties of neural network functions.
    • To establish a relationship between network parameters and their spectral representation.
    • To explore the significance of hidden nodes in determining network function spectra.

    Main Methods:

    • Utilizing Fourier series coefficients of activation functions, truncated and periodically extended.
    • Analyzing the spectrum of network functions under numerical constraints.
    • Employing the Mixed National Institute of Standards and Technology (MNIST) dataset for validation.

    Main Results:

    • Established a high-precision conversion between network parameters and their spectral characteristics.
    • Quantified the impact of hidden nodes on the overall network function spectrum.
    • Demonstrated the practical application of spectral analysis in network interpretation.

    Conclusions:

    • Spectrum analysis provides a powerful lens for interpreting neural network parameters and function.
    • Derived algorithms for parameter initialization and pruning show the practical utility of spectral insights.
    • This work highlights the potential of spectral analysis in advancing neural network interpretability and decision-making.