Structure-preserving GANs
Structure-preserving GANs
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发表时间：
2022-02
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通讯作者：
Jeremiah Birrell;M. Katsoulakis;Luc Rey-Bellet;Wei Zhu
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作者：
Jeremiah Birrell;M. Katsoulakis;Luc Rey-Bellet;Wei Zhu
生成对抗网络（GAN）是一类基于生成器和代理之间的两人游戏的分布学习方法，通常可以基于未知分布和生成分布之间的分歧的变分表示将其表示为极小极大问题。我们引入了结构保持GAN作为一个数据高效的框架，用于学习具有额外结构（如群对称性）的分布，通过开发新的分歧变分表示。我们的理论表明，我们可以减少的σ-空间上的不变σ-空间的投影，使用的条件期望与相关的基础结构的σ-代数。此外，我们证明了减少的空间必须伴随着一个精心设计的结构化发电机，有缺陷的设计可能很容易导致灾难性的“模式崩溃”的教训分布。我们通过为具有内在群对称性的分布构建保持对称性的GAN来构建我们的框架，并证明了两个参与者，即等变生成器和不变子系统，在学习过程中发挥着重要但独特的作用。在广泛的数据集，包括真实世界的医学成像，实证实验和消融研究，验证了我们的理论，并表明我们提出的方法实现了显着提高样本保真度和多样性-几乎一个数量级测量的Fr\'echet初始距离-特别是在小数据制度。
Generative adversarial networks (GANs), a class of distribution-learning methods based on a two-player game between a generator and a discriminator, can generally be formulated as a minmax problem based on the variational representation of a divergence between the unknown and the generated distributions. We introduce structure-preserving GANs as a data-efficient framework for learning distributions with additional structure such as group symmetry, by developing new variational representations for divergences. Our theory shows that we can reduce the discriminator space to its projection on the invariant discriminator space, using the conditional expectation with respect to the sigma-algebra associated to the underlying structure. In addition, we prove that the discriminator space reduction must be accompanied by a careful design of structured generators, as flawed designs may easily lead to a catastrophic"mode collapse"of the learned distribution. We contextualize our framework by building symmetry-preserving GANs for distributions with intrinsic group symmetry, and demonstrate that both players, namely the equivariant generator and invariant discriminator, play important but distinct roles in the learning process. Empirical experiments and ablation studies across a broad range of data sets, including real-world medical imaging, validate our theory, and show our proposed methods achieve significantly improved sample fidelity and diversity -- almost an order of magnitude measured in Fr\'echet Inception Distance -- especially in the small data regime.