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Then

Martín Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. , “Tensorflow: A system for large-scale machine learning.” in OSDI , Vol. 16 (2016) pp. 265–283
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2021

SymmetryGAN: Symmetry Discovery with Deep Learning

Desai, Krish, Nachman, Benjamin, Thaler, Jesse

Understand

What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian factors introduced while changing coordinates.

In this paper, we provide a rigorous statistical definition of the symmetries of a dataset, which involves inertial reference densities, in analogy to inertial frames in classical mechanics.
We then propose SymmetryGAN as a novel and powerful approach to automatically discover symmetries using a deep learning method based on generative adversarial networks (GANs).
When applied to Gaussian examples, SymmetryGAN shows excellent empirical performance, in agreement with expectations from the analytic loss landscape.