Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent | Paper Citation Record

Observation 46861ce3-8316-4f9d-b552-4f45e5b6af44 · outbound

This paper cites A convergence theory for deep learning via over-parameterization.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent A convergence theory for deep learning via over-parameterization

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This paper cites Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks

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This paper cites Spectrally-normalized margin bounds for neural networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Spectrally-normalized margin bounds for neural networks

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This paper cites Convergence rates for shallow neural networks learned by gradient descent.Bernoulli, 30(1):475–502, 2024.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Convergence rates for shallow neural networks learned by gradient descent.Bernoulli, 30(1):475–502, 2024

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This paper cites Stochastic Gradient Descent for Two-layer Neural Networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Stochastic Gradient Descent for Two-layer Neural Networks

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This paper cites Generalization bounds of stochastic gradient descent for wide and deep neural networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Generalization bounds of stochastic gradient descent for wide and deep neural networks

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This paper cites Generalization error bounds of gradient descent for learning over-parameterized deep relu networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Generalization error bounds of gradient descent for learning over-parameterized deep relu networks

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This paper cites Optimal rates for the regularized least-squares algorithm.Foundations of Computational Mathematics, 7(3):331–368, 2007.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Optimal rates for the regularized least-squares algorithm.Foundations of Computational Mathematics, 7(3):331–368, 2007

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This paper cites Learning with sgd and random features.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Learning with sgd and random features

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This paper cites How much over-parameterization is sufficient to learn deep relu networks? InInternational Conference on Learning Representation, 2021.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent How much over-parameterization is sufficient to learn deep relu networks? InInternational Conference on Learning Representation, 2021

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This paper cites Cambridge University Press, 2007.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Cambridge University Press, 2007

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This paper cites Nonparametric stochastic approximation with large step-sizes.Annals of Statistics, 44(4):1363–1399, 2016.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Nonparametric stochastic approximation with large step-sizes.Annals of Statistics, 44(4):1363–1399, 2016

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This paper cites Analysis of the expected $L_2$ error of an over-parametrized deep neural network estimate learned by gradient descent without regularization.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Analysis of the expected $L_2$ error of an over-parametrized deep neural network estimate learned by gradient descent without regularization

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Unresolved cited work

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This paper cites Gradient descent finds global minima of deep neural networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Gradient descent finds global minima of deep neural networks

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This paper cites Random feature amplification: Feature learning and generalization in neural networks.Journal of Machine Learning Research, 24(303):1–49, 2023.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Random feature amplification: Feature learning and generalization in neural networks.Journal of Machine Learning Research, 24(303):1–49, 2023

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This paper cites Size-independent sample complexity of neural networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Size-independent sample complexity of neural networks

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This paper cites Springer Science & Business Media, 2006.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Springer Science & Business Media, 2006

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This paper cites Deep residual learning for image recognition.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Deep residual learning for image recognition

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This paper cites Neural tangent kernel: Convergence and generalization in neural networks.Advances in Neural Information Processing Systems, 31, 2018.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Neural tangent kernel: Convergence and generalization in neural networks.Advances in Neural Information Processing Systems, 31, 2018

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This paper cites Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow relu networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow relu networks

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This paper cites On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent

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This paper cites Learning Lipschitz Functions by GD-trained Shallow Overparameterized ReLU Neural Networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Learning Lipschitz Functions by GD-trained Shallow Overparameterized ReLU Neural Networks

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Stability and generalization analysis of gradient methods for shallow neural networks

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This paper cites Optimization and generalization of gradient descent for shallow ReLU networks with minimal width.Journal of Machine Learning Research, 27(34):1–35, 2026.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Optimization and generalization of gradient descent for shallow ReLU networks with minimal width.Journal of Machine Learning Research, 27(34):1–35, 2026

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This paper cites Optimal rates for generalization of gradient descent for deep relu classification.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Optimal rates for generalization of gradient descent for deep relu classification

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This paper cites Learning overparameterized neural networks via stochastic gradient descent on structured data.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Learning overparameterized neural networks via stochastic gradient descent on structured data

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This paper cites Optimal rates for multi-pass stochastic gradient methods.Journal of Machine Learning Research, 18(1):3375–3421, 2017.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Optimal rates for multi-pass stochastic gradient methods.Journal of Machine Learning Research, 18(1):3375–3421, 2017

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This paper cites On the linearity of large non-linear models: when and why the tangent kernel is constant.Advances in Neural Information Processing Systems, 33:15954–15964, 2020.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent On the linearity of large non-linear models: when and why the tangent kernel is constant.Advances in Neural Information Processing Systems, 33:15954–15964, 2020

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Norm-based capacity control in neural networks

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Random feature approximation for general spectral methods

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This paper cites How many neurons do we need? a refined analysis for shallow networks trained with gradient descent.Journal of Statistical Planning and Inference, page 106169, 2024.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent How many neurons do we need? a refined analysis for shallow networks trained with gradient descent.Journal of Statistical Planning and Inference, page 106169, 2024

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Gradient Descent can Learn Less Over-parameterized Two-layer Neural Networks on Classification Problems

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Optimal rates for averaged stochastic gradient descent under neural tangent kernel regime

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Near-minimax optimal estimation with shallow relu neural networks.IEEE Transactions on Information Theory, 69(2):1125–1140, 2022

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This paper cites Weighted sums of random kitchen sinks: Replacing minimization with random- ization in learning.Advances in Neural Information Processing Systems, 21, 2008.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Weighted sums of random kitchen sinks: Replacing minimization with random- ization in learning.Advances in Neural Information Processing Systems, 21, 2008

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Searching for Activation Functions

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Stability & generalisation of gradient descent for shallow neural networks without the neural tangent kernel

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This paper cites Springer Science & Business Media, 2008.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Springer Science & Business Media, 2008

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Generalization and stability of interpolating neural networks with minimal width.Journal of Machine Learning Research, 25(156):1–41, 2024

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Sharper guarantees for learning neural network classifiers with gradient methods, 2025

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Cambridge university press, 2018

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This paper cites Cambridge university press, 2019.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Cambridge university press, 2019

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This paper cites Generalization guarantees of gradient descent for shallow neural networks.Neural Computation, 37(2):344–402, 2025.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Generalization guarantees of gradient descent for shallow neural networks.Neural Computation, 37(2):344–402, 2025

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This paper cites Population Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Population Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise

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This paper cites Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Unresolved cited work

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This paper cites Learning bounds for kernel regression using effective data dimensionality.Neural computation, 17(9):2077–2098, 2005.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Learning bounds for kernel regression using effective data dimensionality.Neural computation, 17(9):2077–2098, 2005

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Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks

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This paper cites Their equation (47) is guaranteed by Lemma 18 with κ2 =∥K∥ ∞, Γ =n , δ=δ 2, ζi =K xi, Q= R X Kx ⊗K xdρx.

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent Their equation (47) is guaranteed by Lemma 18 with κ2 =∥K∥ ∞, Γ =n , δ=δ 2, ζi =K xi, Q= R X Kx ⊗K xdρx

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