Abstract
A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves the interpretability and the functionality of learned representations both using stochastic and deterministic generators.
Original language | English |
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Title of host publication | Proceedings of the 24th International Conference on Artificial Intelligence and Statistics |
Number of pages | 10 |
Publisher | International Machine Learning Society (IMLS) |
Publication date | 2021 |
Publication status | Published - 2021 |
Event | 24th International Conference on Artificial Intelligence and Statistics - Virtual Conference Duration: 13 Apr 2021 → 15 Apr 2021 https://aistats.org/aistats2021/ |
Conference
Conference | 24th International Conference on Artificial Intelligence and Statistics |
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Location | Virtual Conference |
Period | 13/04/2021 → 15/04/2021 |
Internet address |
Series | Proceedings of Machine Learning Research |
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Volume | 130 |
ISSN | 2640-3498 |