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The manifold hypothesis states that high-dimensional data can be modeled as lying on or near a low-dimensional, nonlinear manifold.
Diffusion variational autoencoders
Rey, L. A. P., Menkovski, V., and Portegies, J. W. (2019) · 1901
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Sparse coding with an overcomplete basis set: A strategy employed by v1?
Olshausen, B. A. and Field, D. J. (1997) · 1997
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Gradient-based learning applied to document recognition
LeCun, Y., Bottou, L., Bengio, Y., Haffner, P., et al. (1998) · 1998
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Nonlinear dimensionality reduction by locally linear embedding
Roweis, S. T. and Saul, L. K. (2000) · 2000
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A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, J. B., De Silva, V., and Langford, J. C. (2000) · 2000
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Non-local manifold tangent learning
Bengio, Y. and Monperrus, M. (2005) · 2005
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Learning to traverse image manifolds
Dollár, P., Rabaud, V., and Belongie, S. J. (2007) · 2007
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Learning transport operators for image manifolds
Culpepper, B. J. and Olshausen, B. A. (2009) · 2009
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Auto-encoding variational bayes
Kingma, D. P. and Welling, M. (2013) · 2013
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Generative adversarial nets
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Stochastic backpropagation and approximate inference in deep generative models
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Importance weighted autoencoders
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J. (2015) · 2015
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Testing the manifold hypothesis
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Unsupervised representation learning with deep convolutional generative adversarial networks
Radford, A., Metz, L., and Chintala, S. (2016) · 2016
The riemannian geometry of deep generative models
Shao, H., Kumar, A., and Thomas Fletcher, P. (2018) · 2018
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Tomczak, J. and Welling, M. (2018) · 2018
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Reparameterizing distributions on lie groups
Falorsi, L., de Haan, P., Davidson, T. R., and Forré, P. (2019) · 2019
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Continuous hierarchical representations with poincaré variational auto-encoders
Mathieu, E., Le Lan, C., Maddison, C. J., Tomioka, R., and Teh, Y. W. (2019) · 2019
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A wrapped normal distribution on hyperbolic space for gradient-based learning
Nagano, Y., Yamaguchi, S., Fujita, Y., and Koyama, M. (2019) · 2019
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Representing closed transformation paths in encoded network latent space
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Latent space oddity: on the curvature of deep generative models
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Metrics for deep generative models
Chen, N., Klushyn, A., Kurle, R., Jiang, X., Bayer, J., and Smagt, P. (2018) · 2018
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Hyperspherical variational auto-encoders
Davidson, T. R., Falorsi, L., De Cao, N., Kipf, T., and Tomczak, J. M. (2018) · 2018
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Connor, M. and Rozell, C. (2020) · 2020
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Variational autoencoders with riemannian brownian motion priors
Kalatzis, D., Eklund, D., Arvanitidis, G., and Hauberg, S. (2020) · 2020
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Variational diffusion autoencoders with random walk sampling
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Mixed-curvature variational autoencoders
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