生成对抗网络（GAN）的收敛性理论分析与改进方向 -计算机科学与技术专业

摘要

生成对抗网络（GAN）作为深度学习领域的重要模型，近年来在图像生成、数据增强等方面展现出卓越性能，但其训练过程中的不稳定性及收敛性问题仍是研究热点。本研究旨在深入分析GAN的收敛性理论，并提出针对性改进策略以优化其训练效果。通过结合博弈论与优化理论，我们系统探讨了GAN中生成器与判别器之间的动态平衡机制，揭示了传统GAN训练过程中可能出现的模式崩塌和梯度消失等问题的根源。所提出的改进方法能够在多种复杂场景下有效缓解训练不稳定性，同时保持生成样本的多样性与真实性。本研究的主要贡献在于从理论层面阐明了GAN收敛性的关键影响因素，并通过实证分析验证了改进方案的有效性，为未来GAN模型的设计与应用提供了重要参考。

关键词：生成对抗网络；收敛性分析；模式崩塌；正则化技术；自适应学习率调整

Theoretical Analysis of Convergence in Generative Adversarial Networks (GAN) and Directions for Improvement

英文人名

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Abstract

Generative adversarial network (GAN), as an important model in the field of deep learning, has shown excellent performance in image generation and data enhancement in recent years, but its instability and convergence in the training process are still hot issues. The purpose of this study is to analyze the convergence theory of GAN, and propose specific improvement strategies to optimize its training effect. By combining game theory and optimization theory, we systematically discuss the dynamic balance mechanism between generator and discriminator in GAN, and reveal the root causes of the problems that may occur in the traditional GAN training process, such as mode collapse and gradient disappearance. The proposed improved method can effectively alleviate the training instability in a variety of complex scenarios, while maintaining the diversity and authenticity of the generated samples. The main contribution of this study is to clarify the key influencing factors of GAN convergence from the theoretical level, and verify the effectiveness of the improved scheme through empirical analysis, which provides an important reference for the future design and application of GAN models.

Keywords: Generative Adversarial Network；Convergence Analysis；Mode Collapse；Regularization Technique；Adaptive Learning Rate Adjustment

引言 1

一、GAN收敛性理论基础分析 1

(一)GAN的基本原理与架构 1

(二)收敛性的定义与衡量标准 2

(三)现有理论的局限性探讨 2

二、GAN收敛性的影响因素研究 3

(一)数据分布对收敛性的作用 3

(二)损失函数设计与收敛关系 3

(三)优化算法对收敛速度的影响 4

三、当前GAN收敛性改进方法综述 4

(一)基于正则化的改进策略 4