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We provide (high probability) bounds on the condition number of random feature matrices.
Random features for large-scale kernel machines
Rahimi, A. and Recht, B · 2007
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Uniform approximation of functions with random bases
Rahimi, A., and Recht, B · 2008
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Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning
Rahimi, A., and Recht, B · 2008
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The spectrum of kernel random matrices
El Karoui, Noureddine · 2010
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The spectrum of random inner-product kernel matrices
Cheng, Xiuyuan and Singer, Amit · 2010
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To understand deep learning we need to understand kernel learning
Belkin, Mikhail and Ma, Siyuan and Mandal, Soumik · 2012
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A mathematical introduction to compressive sensing
Foucart, Simon and Rauhut, Holger · 2013
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Sparse random feature algorithm as coordinate descent in Hilbert space
Yen, Ian En-Hsu and Lin, Ting-Wei and Lin, Shou-De and Ravikumar, Pradeep K and Dhillon, Inderjit S · 2014
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Less is More: Nyström Computational Regularization
Li, Zhu and Ton, Jean-Francois and Oglic, Dino and Sejdinovic, Dino · 2015
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Generalization Properties of Learning with Random Features
Rudi, Alessandro and Rosasco, Lorenzo · 2017
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Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice
Pennington, Jeffrey and Schoenholz, Samuel S and Ganguli, Surya · 2017
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Stable architectures for deep neural networks
Haber, Eldad and Ruthotto, Lars · 2017
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On the equivalence between kernel quadrature rules and random feature expansions
Bach, Francis · 2017
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A random matrix approach to neural networks
Louart, Cosme and Liao, Zhenyu and Couillet, Romain · 2018
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On the spectrum of random features maps of high dimensional data
Liao, Zhenyu and Couillet, Romain · 2018
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The lottery ticket hypothesis: Finding sparse, trainable neural networks
Frankle, Jonathan and Carbin, Michael · 2018
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Towards a unified analysis of random Fourier features
Li, Z., Ton, J.-F., Oglic, D., and Sejdinovic, D · 2019
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Reconciling modern machine-learning practice and the classical bias–variance trade-off
Belkin, Mikhail and Hsu, Daniel and Ma, Siyuan and Mandal, Soumik · 2019
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Does data interpolation contradict statistical optimality?
Belkin, Mikhail and Rakhlin, Alexander and Tsybakov, Alexandre B · 2019
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Surprises in high-dimensional ridgeless least squares interpolation
Benign overfitting in linear regression
Bartlett, Peter L and Long, Philip M and Lugosi, Gábor and Tsigler, Alexander · 2020
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Benign overfitting in ridge regression
Hastie, Trevor and Montanari, Andrea and Rosset, Saharon and Tibshirani, Ryan J · 2020
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Just interpolate: Kernel “ridgeles” regression can generalize
Liang, Tengyuan and Rakhlin, Alexander · 2020
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Two models of double descent for weak features
Belkin, Mikhail and Hsu, Daniel and Xu, Ji · 2020
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On the multiple descent of minimum-norm interpolants and restricted lower isometry of kernels
Liang, Tengyuan and Rakhlin, Alexander and Zhai, Xiyu · 2020
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The slow deterioration of the generalization error of the random feature model
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Hastie, Trevor and Montanari, Andrea and Rosset, Saharon and Tibshirani, Ryan J · 2019
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The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve
Mei, Song and Montanari, Andrea · 2019
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The spectral norm of random inner-product kernel matrices
Fan, Zhou and Montanari, Andrea · 2019
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Nonlinear random matrix theory for deep learning
Pennington, Jeffrey and Worah, Pratik · 2019
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Double descent in the condition number
Poggio, Tomaso and Kur, Gil and Banburski, Andrzej · 2019
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Generalization of two-layer neural networks: An asymptotic viewpoint
Ba, Jimmy and Erdogdu, Murat and Suzuki, Taiji and Wu, Denny and Zhang, Tianzong · 2019
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Eigenvalue distribution of nonlinear models of random matrices
Benigni, Lucas and Péché, Sandrine · 2019
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Ma, Chao and Wu, Lei and E, Weinan · 2020
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Forward stability of ResNet and its variants
Zhang, Linan and Schaeffer, Hayden · 2020
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Liao, Zhenyu and Couillet, Romain and Mahoney, Michael W · 2020
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On random matrices arising in deep neural networks. gaussian case
Pastur, Leonid · 2020
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High-dimensional dynamics of generalization error in neural networks
Advani, Madhu S and Saxe, Andrew M and Sompolinsky, Haim · 2020
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Avoiding The Double Descent Phenomenon of Random Feature Models Using Hybrid Regularization
Kan, Kelvin and Nagy, James G and Ruthotto, Lars · 2020
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Generalization Bounds for Sparse Random Feature Expansions
Hashemi, Abolfazl and Schaeffer, Hayden and Shi, Robert and Topcu, Ufuk and Tran, Giang and Ward, Rachel · 2021
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Mei, Song and Misiakiewicz, Theodor and Montanari, Andrea · 2021
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