Flat metric minimization with applications in generative modeling

Möllenhoff T, Cremers D (2019)

Publication Type: Conference contribution

Publication year: 2019

Publisher: International Machine Learning Society (IMLS)

Book Volume: 2019-June

Pages Range: 8137-8148

Conference Proceedings Title: 36th International Conference on Machine Learning, ICML 2019

Event location: Long Beach, CA, USA

ISBN: 9781510886988

Abstract

We take the novel perspective to view data not as a probability distribution but rather as a current. Primarily studied in the field of geometric measure theory, k-currents are continuous linear functionals acting on compactly supported smooth differential forms and can be understood as a generalized notion of oriented k-dimensional manifold. By moving from distributions (which are 0-currents) to k-currents, we can explicitly orient the data by attaching a k-dimensional tangent plane to each sample point. Based on the flat metric which is a fundamental distance between currents, we derive FlatGAN, a formulation in the spirit of generative adversarial networks but generalized to k-currents. In our theoretical contribution we prove that the flat metric between a parametrized current and a reference current is Lipschitz continuous in the parameters. In experiments, we show that the proposed shift to k > 0 leads to interpretable and disentangled latent representations which behave equivariantly to the specified oriented tangent planes.

Involved external institutions

Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Möllenhoff, T., & Cremers, D. (2019). Flat metric minimization with applications in generative modeling. In 36th International Conference on Machine Learning, ICML 2019 (pp. 8137-8148). Long Beach, CA, USA: International Machine Learning Society (IMLS).

MLA:

Möllenhoff, Thomas, and Daniel Cremers. "Flat metric minimization with applications in generative modeling." Proceedings of the 36th International Conference on Machine Learning, ICML 2019, Long Beach, CA, USA International Machine Learning Society (IMLS), 2019. 8137-8148.

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