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In deep learning it is common to overparameterize neural networks, that is, to use more parameters than training samples.
The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
L. Bregman · 1967
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Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
E. J. Candès, J. Romberg, and T. Tao · 2006
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Stable signal recovery from incomplete and inaccurate measurements
E. J. Candès, J. K. Romberg, and T. Tao · 2006
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Compressed sensing
D. L. Donoho · 2006
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A Mathematical Introduction to Compressive Sensing
S. Foucart and H. Rauhut · 2013
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In search of the real inductive bias: On the role of implicit regularization in deep learning
B. Neyshabur, R. Tomioka, and N. Srebro · 2015
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Implicit regularization in matrix factorization
S. Gunasekar, B. E. Woodworth, S. Bhojanapalli, B. Neyshabur, and N. Srebro · 2017
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Lasso, fractional norm and structured sparse estimation using a Hadamard product parametrization
P. D. Hoff · 2017
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Geometry of optimization and implicit regularization in deep learning
B. Neyshabur, R. Tomioka, R. Salakhutdinov, and N. Srebro · 2017
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Understanding deep learning requires rethinking generalization
C. Zhang, S. Bengio, M. Hardt, B. Recht, and O. Vinyals · 2017
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On the optimization of deep networks: Implicit acceleration by overparameterization
S. Arora, N. Cohen, and E. Hazan · 2018
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Implicit bias of gradient descent on linear convolutional networks
S. Gunasekar, J. D. Lee, D. Soudry, and N. Srebro · 2018
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Improved bounds for sparse recovery from subsampled random convolutions
S. Mendelson, H. Rauhut, and R. Ward · 2018
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The implicit bias of gradient descent on separable data
D. Soudry, E. Hoffer, M. S. Nacson, S. Gunasekar, and N. Srebro · 2018
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Implicit regularization in deep matrix factorization
S. Arora, N. Cohen, W. Hu, and Y. Luo · 2019
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Implicit regularization of discrete gradient dynamics in linear neural networks
G. Gidel, F. Bach, and S. Lacoste-Julien · 2019
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Implicit regularization for optimal sparse recovery
T. Vaskevicius, V. Kanade, and P. Rebeschini · 2019
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Implicit regularization via hadamard product over-parametrization in high-dimensional linear regression
P. Zhao, Y. Yang, and Q.-C. He · 2019
A continuous-time mirror descent approach to sparse phase retrieval
F. Wu and P. Rebeschini · 2020
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On the implicit bias of initialization shape: Beyond infinitesimal mirror descent
S. Azulay, E. Moroshko, M. S. Nacson, B. E. Woodworth, N. Srebro, A. Globerson, and D. Soudry · 2021
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Sparse recovery in bounded riesz systems with applications to numerical methods for pdes
S. Brugiapaglia, S. Dirksen, H. C. Jung, and H. Rauhut · 2021
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Mirrorless mirror descent: A natural derivation of mirror descent
S. Gunasekar, B. Woodworth, and N. Srebro · 2021
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Implicit sparse regularization: The impact of depth and early stopping
J. Li, T. Nguyen, C. Hegde, and K. W. Wong · 2021
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Implicit regularization in tensor factorization
N. Razin, A. Maman, and N. Cohen · 2021
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Gradient descent for deep matrix factorization: Dynamics and implicit bias towards low rank
H. Chou, C. Gieshoff, J. Maly, and H. Rauhut · 2020
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Low-rank regularization and solution uniqueness in over-parameterized matrix sensing
K. Geyer, A. Kyrillidis, and A. Kalev · 2020
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The implicit bias of depth: How incremental learning drives generalization
D. Gissin, S. Shalev-Shwartz, and A. Daniely · 2020
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Implicit regularization in deep learning may not be explainable by norms
N. Razin and N. Cohen · 2020
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Kernel and rich regimes in overparametrized models
B. Woodworth, S. Gunasekar, J. D. Lee, E. Moroshko, P. Savarese, I. Golan, D. Soudry, and N. Srebro · 2020
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Small random initialization is akin to spectral learning : Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction
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Hadamard Wirtinger flow for sparse phase retrieval
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Implicit regularization in matrix sensing via mirror descent
F. Wu and P. Rebeschini · 2021
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Implicit regularization in hierarchical tensor factorization and deep convolutional neural networks
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Large learning rate tames homogeneity: Convergence and balancing effect
Y. Wang, M. Chen, T. Zhao, and M. Tao · 2022
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