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This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data.
Invariant variation problems
E. Noether · 1971
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Classical Mechanics
H. Goldstein · 1980
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Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel · 1989
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An introduction to Lie groups and Lie algebras , volume 113
A. A. Kirillov · 2008
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Density estimation by dual ascent of the log-likelihood
E. G. Tabak, E. Vanden-Eijnden, et al · 2010
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Mcmc using hamiltonian dynamics
R. M. Neal et al · 2011
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Representation learning: A review and new perspectives
Y. Bengio, A. Courville, and P. Vincent · 2013
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D. P. Kingma and M. Welling · 2013
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D. P. Kingma and J. Ba · 2014
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Variational inference with normalizing flows
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β \beta -vae: Learning basic visual concepts with a constrained variational framework
I. Higgins, L. Matthey, A. Pal, C. Burgess, X. Glorot, M. Botvinick, S. Mohamed, and A. Lerchner · 2017
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Generalizing hamiltonian monte carlo with neural networks
D. Levy, M. D. Hoffman, and J. Sohl-Dickstein · 2017
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Masked autoregressive flow for density estimation
G. Papamakarios, T. Pavlakou, and I. Murray · 2017
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Towards a definition of disentangled representations
I. Higgins, D. Amos, D. Pfau, S. Racaniere, L. Matthey, D. J. Rezende, and A. Lerchner · 2018
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D. Jimenez Rezende and F. Viola · 2018
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L. Dinh, J. Sohl-Dickstein, and S. Bengio · 2016
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Normalizing flows on riemannian manifolds
M. C. Gemici, D. Jimenez Rezende, and S. Mohamed · 2016
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Improved variational inference with inverse autoregressive flow
D. P. Kingma, T. Salimans, R. Jozefowicz, X. Chen, I. Sutskever, and M. Welling · 2016
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Isolating sources of disentanglement in variational autoencoders
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Neural ordinary differential equations
T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. K. Duvenaud
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Glow: Generative flow with invertible 1x1 convolutions
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Flow-based generative models for markov chain monte carlo in lattice field theory
M. Albergo, G. Kanwar, and P. Shanahan · 2019
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