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Paper · 2101.06006 · ICLR · 2021

The Geometry of Deep Generative Image Models and its Applications

Binxu Wang, Carlos Ponce

arXiv · PDF · Open in the Atlas

Code that ran

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RepositoryRoleRan
Animadversio/GAN-Geometry canonical 0 of 1
copy not recorded — 2 of 2
rosinality/stylegan2-pytorch reimplementation 1 of 1
FunctionStatusWhere it lives
get_lr Ran this paper's copy was not recorded; identical code first harvested from mbbrodie/stylegan2
pointer only · get_code("ea6c82ed6a138df9")
latent_noise Ran this paper's copy was not recorded; identical code first harvested from mbbrodie/stylegan2
pointer only · get_code("a73e1d557a70850c")
noise_regularize Ran rosinality/stylegan2-pytorch/projector.py
code served (permissive licence) · get_code("ba1ee6c930acf688")
hessian_compute Not yet run Animadversio/GAN-Geometry/core/GAN_hessian_compute.py
pointer only (licence: NONE) · get_code("55a3044d4448ba0b")

Repositories linked to this paper

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Abstract

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, limiting 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.

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