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arXiv 2101.06006cs.LGcs.NAcs.NEmath.NA
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深生成图像模型的几何及其应用

The Geometry of Deep Generative Image Models and its Applications

Washington University in St Louis(圣路易斯华盛顿大学);Department of Neuroscience(神经科学系)

Binxu Wang, Carlos R. Ponce

摘要:

生成对抗网络(GANs)已经成为一种强大的无监督方法,可以对真实世界数据集(如自然图像)的统计模式进行建模。这些网络经过训练,将其潜在空间中的随机输入映射到代表学习数据的新样本。然而,由于潜在空间的高维性和生成器的非线性,潜在空间的结构很难直观,这限制了模型的实用性。理解潜在空间需要一种方法来识别现有真实世界图像的输入代码(反演),以及一种方法来识别已知图像变换的方向(可解释性)。在这里,我们使用几何框架来同时解决这两个问题。我们开发了一种与架构无关的方法来计算由GANs创建的图像流形的黎曼度量。度量的特征分解隔离了说明不同水平的图像变化的轴。对几个预训练的GANs的实证分析表明,每个位置周围的图像变化都集中在令人惊讶的少数主轴上(空间是高度各向异性的),并且在空间的不同位置上产生这种大变化的方向是相似的(空间是均匀的)。我们发现,许多顶部的特征向量对应于图像空间中的可解释的变换,与本征空间的很大一部分对应于可以被压缩出来的未成年人的变换。这种几何理解统一了以前与GAN可解释性相关的关键结果。我们表明,使用这个度量允许更有效的优化在潜在的空间(例如GAN反演),并促进无监督的发现可解释的轴。我们的研究结果表明,定义GAN图像流形的几何形状可以作为理解GANs的一般框架。

英文摘要:

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space to new samples representative of the learned data. However, the structure of the latent space is hard to intuit due to its high dimensionality and the non-linearity of the generator, which limits the usefulness of the models. Understanding the latent space requires a way to identify input codes for existing real-world images (inversion), and a way to identify directions with known image transformations (interpretability). Here, we use a geometric framework to address both issues simultaneously. We develop an architecture-agnostic method to compute the Riemannian metric of the image manifold created by GANs. The eigen-decomposition of the metric isolates axes that account for different levels of image variability. An empirical analysis of several pretrained GANs shows that image variation around each position is concentrated along surprisingly few major axes (the space is highly anisotropic) and the directions that create this large variation are similar at different positions in the space (the space is homogeneous). We show that many of the top eigenvectors correspond to interpretable transforms in the image space, with a substantial part of eigenspace corresponding to minor transforms which could be compressed out. This geometric understanding unifies key previous results related to GAN interpretability. We show that the use of this metric allows for more efficient optimization in the latent space (e.g. GAN inversion) and facilitates unsupervised discovery of interpretable axes. Our results illustrate that defining the geometry of the GAN image manifold can serve as a general framework for understanding GANs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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