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We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space.
On lines and planes of closest fit to systems of points in space
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Lambertian reflectance and linear subspaces
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Laplacian eigenmaps for dimensionality reduction and data representation
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Video-based face recognition using probabilistic appearance manifolds
Lee, Kuang-Chih, Ho, Jeffrey, Yang, Ming-Hsuan, and Kriegman, David · 2003
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On the number of linear regions of deep neural networks
Montufar, G. F., Pascanu, R., Cho, K., and Bengio, Y · 2014
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Deep metric learning for person re-identification
Yi, D., Lei, Z., Liao, S., and Li, S. Z · 2014
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On the expressive power of deep learning: A tensor analysis, 2015
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The power of depth for feedforward neural networks
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Nonlinear metric learning with deep convolutional neural network for face verification
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Provable approximation properties for deep neural networks
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Representation benefits of deep feedforward networks
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Deep neural networks with random gaussian weights: A universal classification strategy?
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