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2020

Learning a Lie Algebra from Unlabeled Data Pairs

Ick, Christopher, Lostanlen, Vincent

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Deep convolutional networks (convnets) show a remarkable ability to learn disentangled representations.

In recent years, the generalization of deep learning to Lie groups beyond rigid motion in $\mathbb{R}^n$ has allowed to build convnets over datasets with non-trivial symmetries, such as patterns over the surface of a sphere.
However, one limitation of this approach is the need to explicitly define the Lie group underlying the desired invariance property before training the convnet.
Whereas rotations on the sphere have a well-known symmetry group ($\mathrm{SO}(3)$), the same cannot be said of many real-world factors of variability.

Learning a Lie Algebra from Unlabeled Data Pairs · Around

Built on

Brian C. Hall. Lie Groups, Lie Algebras, and Representations . Springer, 2000
Original
2000
Earlier work this paper cites.
Ian Goodfellow, Aaron Courville, and Yoshua Bengio. Deep learning . MIT Press, 2016
2016
Earlier work this paper cites.
Stéphane Mallat. Understanding deep convolutional networks . Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065), 2016
2016
Earlier work this paper cites.

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Then

Taco S. Cohen, Mario Geiger, Jonas Koehler, Max Welling Spherical CNNs. Proceedings of the 6th International Conference on Learning Representations (ICLR) , 2018
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