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In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low.
Decoding by linear programming
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Simultaneous analysis of lasso and dantzig selector
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Oracle inequalities and optimal inference under group sparsity
Karim Lounici, Massimiliano Pontil, Sara Van De Geer, and Alexandre B Tsybakov · 2011
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High-dimensional probability: An introduction with applications in data science , volume 47
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Reconciling modern machine-learning practice and the classical bias–variance trade-off
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Gradient descent provably optimizes over-parameterized neural networks
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Partha P Mitra · 2019
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Implicit regularization for optimal sparse recovery
Tomas Vaskevicius, Varun Kanade, and Patrick Rebeschini · 2019
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Benign overfitting in linear regression
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Minimum ℓ 1 \ell_{1} -norm interpolators: Precise asymptotics and multiple descent
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Implicit regularization in tensor factorization
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Foolish crowds support benign overfitting
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Surprises in high-dimensional ridgeless least squares interpolation
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Implicit bias of gradient descent on reparametrized models: On equivalence to mirror descent
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Implicit regularization in hierarchical tensor factorization and deep convolutional neural networks
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Tight bounds for minimum ℓ 1 \ell_{1} -norm interpolation of noisy data
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Implicit bias in leaky relu networks trained on high-dimensional data
Spencer Frei, Gal Vardi, Peter Bartlett, Nathan Srebro, and Wei Hu · 2023
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Implicit regularization towards rank minimization in relu networks
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