This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the L2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features.
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InvNet: Encoding Geometric and Statistical Invariances in Deep Generative Models
Generative Adversarial Networks (GANs), while widely successful in modeling complex data distributions, have not yet been sufficiently leveraged in scientific computing and design. Reasons for this include the lack of flexibility of GANs to represent discrete-valued image data, as well as the lack of control over physical properties of generated samples. We propose a new conditional generative modeling approach (InvNet) that efficiently enables modeling discrete-valued images, while allowing control over their parameterized geometric and statistical properties. We evaluate our approach on several synthetic and real world problems: navigating manifolds of geometric shapes with desired sizes; generation of binary two-phase materials; and the (challenging) problem of generating multi-orientation polycrystalline microstructures.
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- Award ID(s):
- 2005804
- PAR ID:
- 10215445
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 34
- Issue:
- 04
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 4377 to 4384
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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