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An Automatic Control Perspective on Parameterizing Generative Adversarial Network.

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    Control theory offers new solutions for generative adversarial networks (GANs), addressing instability and mode collapse. New PID controllers enhance GAN stability and image generation quality, even with limited data.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Control Theory

    Background:

    • Generative Adversarial Networks (GANs) face challenges with instability and mode collapse.
    • Existing GANs lack robust theoretical frameworks for stability analysis.

    Purpose of the Study:

    • To apply control theory principles to understand and resolve GAN instability and mode collapse.
    • To develop novel GAN architectures with guaranteed stability and improved performance.

    Main Methods:

    • Parameterizing GAN dynamics in function space for control-directed analysis.
    • Utilizing linear control theory to analyze GAN stability based on control parameters.
    • Designing Proportional-Integral-Derivative (PID) controllers for enhanced GAN stability.
    • Developing nonlinear control theory-based models (NPIDGAN) for improved GAN performance.

    Main Results:

    • Stability of GANs is proven to depend solely on control parameters.
    • PID controllers enable adaptive image generation with controlled overshoot.
    • Novel PIDGAN and NPIDGAN models demonstrate theoretical stability guarantees.
    • Proposed models achieve superior performance at 1024x1024 resolution across diverse datasets, outperforming state-of-the-art GANs, especially with limited data.

    Conclusions:

    • Control theory provides a powerful framework for analyzing and improving GANs.
    • PIDGAN and NPIDGAN effectively mitigate instability and mode collapse.
    • The proposed methods offer enhanced stability and superior image generation quality, even in data-scarce scenarios.