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Non-exhaustive Learning Using Gaussian Mixture Generative Adversarial Networks Read chapter Read first chapter

2021 | OriginalPaper | Chapter

CycleGAN Through the Lens of (Dynamical) Optimal Transport

Authors : Emmanuel de Bézenac, Ibrahim Ayed, Patrick Gallinari

Published in: Machine Learning and Knowledge Discovery in Databases. Research Track

Publisher: Springer International Publishing

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Abstract

Unsupervised Domain Translation (UDT) is the problem of finding a meaningful correspondence between two given domains, without explicit pairings between elements of the domains. Following the seminal CycleGAN model, variants and extensions have been used successfully for a wide range of applications. However, although there have been some attempts, they remain poorly understood, and lack theoretical guarantees. In this work, we explore the implicit biases present in current approaches and demonstrate where and why they fail. By expliciting these biases, we show that UDT can be reframed as an Optimal Transport (OT) problem. Using the dynamical formulation of Optimal Transport, this allows us to improve the CycleGAN model into a simple and practical formulation which comes with theoretical guarantees and added robustness. Finally, we show how our improved model behaves on the CelebA dataset in a standard then in a more challenging setting, thus paving the way for new applications of UDT. Supplementary material is available at https://​arxiv.​org/​pdf/​1906.​01292.

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previous chapter Principled Interpolation in Normalizing Flows
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Footnotes
1
The push-forward measure \(f_\sharp \rho \) is defined as \({f_\sharp \rho (B) = \rho (f^{-1}(B))}\), for any measurable set B. Said otherwise, we need T to map \({\alpha }\) to \({\beta }\) and S does the reverse.
 
2
A larger family of costs can be considered at the expense of some technicalities, see [13].
 
3
Which was pioneered in [5] and for which a detailed modern presentation is given in chapters 4 and 5 of [22].
 
4
Other schemes could be used, which would lead to other architectures, and could arguably be more suited for stability reasons but this is beyond the scope of this work.
 
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Metadata
Title
CycleGAN Through the Lens of (Dynamical) Optimal Transport
Authors
Emmanuel de Bézenac
Ibrahim Ayed
Patrick Gallinari
Copyright Year
2021
Book
Machine Learning and Knowledge Discovery in Databases. Research Track

Print ISBN: 978-3-030-86519-1

Electronic ISBN: 978-3-030-86520-7

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-86520-7_9

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