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Penalizing the nuclear norm of a function's Jacobian encourages it to locally behave like a low-rank linear map.
A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
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Nonlinear total variation based noise removal algorithms
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Functional approximation by feed-forward networks: a least-squares approach to generalization
A. Webb · 1994
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Training with noise is equivalent to tikhonov regularization
C. M. Bishop · 1995
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A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics
D. Martin, C. Fowlkes, D. Tal, and J. Malik · 2001
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Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
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Fast maximum margin matrix factorization for collaborative prediction
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Image denoising by sparse 3-d transform-domain collaborative filtering
K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian · 2007
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Extracting and composing robust features with denoising autoencoders
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Matrix completion from a few entries
R. H. Keshavan, S. Oh, and A. Montanari · 2009
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A singular value thresholding algorithm for matrix completion
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The power of convex relaxation: near-optimal matrix completion
E. J. Candès and T. Tao · 2010
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Spectral regularization algorithms for learning large incomplete matrices
R. Mazumder, T. Hastie, and R. Tibshirani · 2010
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Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion
P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, P.-A. Manzagol, and L. Bottou · 2010
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Robust principal component analysis?
E. J. Candès, X. Li, Y. Ma, and J. Wright · 2011
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A simpler approach to matrix completion
B. Recht · 2011
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Contractive auto-encoders: Explicit invariance during feature extraction
S. Rifai, P. Vincent, X. Muller, X. Glorot, and Y. Bengio · 2011
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Exact matrix completion via convex optimization
E. Candès and B. Recht · 2012
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Unifying nuclear norm and bilinear factorization approaches for low-rank matrix decomposition
R. Cabral, F. De la Torre, J. P. Costeira, and A. Bernardino · 2013
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Reconstruction of a low-rank matrix in the presence of gaussian noise
A. Shabalin and A. Nobel · 2013
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What regularized auto-encoders learn from the data-generating distribution
G. Alain and Y. Bengio · 2014
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Gradient regularization improves accuracy of discriminative models
D. Varga, A. Csiszárik, and Z. Zombori · 2017
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Neural ordinary differential equations
R. T. Chen, Y. Rubanova, J. Bettencourt, and D. K. Duvenaud · 2018
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Nuclear norm as minimum of frobenius norm product
T. Fritz · 2018
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Improving dnn robustness to adversarial attacks using jacobian regularization
D. Jakubovitz and R. Giryes · 2018
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Noise2noise: Learning image restoration without clean data
J. Lehtinen, J. Munkberg, J. Hasselgren, S. Laine, T. Karras, M. Aittala, and T. Aila · 2018
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Decoupled weight decay regularization
I. Loshchilov and F. Hutter · 2019
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A simple prior-free method for non-rigid structure-from-motion factorization
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The optimal hard threshold for singular values is 4 / 3 4/\sqrt{3}
M. Gavish and D. L. Donoho · 2014
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Optshrink: An algorithm for improved low-rank signal matrix denoising by optimal, data-driven singular value shrinkage
R. Nadakuditi · 2014
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Deep learning face attributes in the wild
Z. Liu, P. Luo, X. Wang, and X. Tang · 2015
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U-net: Convolutional networks for biomedical image segmentation
O. Ronneberger, P. Fischer, and T. Brox · 2015
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ImageNet Large Scale Visual Recognition Challenge
O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, and L. Fei-Fei · 2015
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C. Finlay, J.-H. Jacobsen, L. Nurbekyan, and A. M. Oberman · 2020
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Robust learning with jacobian regularization, 2020
J. Hoffman, D. A. Roberts, and S. Yaida · 2020
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Learning differential equations that are easy to solve
J. Kelly, J. Bettencourt, M. J. Johnson, and D. K. Duvenaud · 2020
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Fourier features let networks learn high frequency functions in low dimensional domains
M. Tancik, P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J. Barron, and R. Ng · 2020
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High-resolution image synthesis with latent diffusion models, 2021
R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer · 2021
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Plug-and-play image restoration with deep denoiser prior
K. Zhang, Y. Li, W. Zuo, L. Zhang, L. Van Gool, and R. Timofte · 2021
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Image denoising: The deep learning revolution and beyond—a survey paper
M. Elad, B. Kawar, and G. Vaksman · 2023
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Generalization in diffusion models arises from geometry-adaptive harmonic representations
Z. Kadkhodaie, F. Guth, E. P. Simoncelli, and S. Mallat · 2024
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