Logarithmic Sobolev Inequalities

Follow this topic Ask about this topic

Recent momentum

emerging

1 papers in the last 28 days · 0.0% of indexed attention

Twelve weeks of publication activity for this topic as it is defined today.

Weekly history

Recent digests

What was published in this topic, kept on the site without email delivery.

Period ending 2026-09-21

1 new paper

A weekly snapshot of new work published in Logarithmic Sobolev Inequalities.

Period ending 2026-09-14

2 new papers

A weekly snapshot of new work published in Logarithmic Sobolev Inequalities.

Period ending 2026-09-07

4 new papers

A weekly snapshot of new work published in Logarithmic Sobolev Inequalities.

20 papers

Latest in Logarithmic Sobolev Inequalities

Open your feed →

Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks
Sep 17, 2026Xianjun Li, Yunfei YangLogarithmic Sobolev Inequalities Rectified Linear Unit Networks
Near-Optimal Learning of Gaussian Sobolev Operators
Jul 8, 2026Ben Adcock, Michael Griebel, Gregor MaierLogarithmic Sobolev Inequalities Probabilistic Operator Learning
Tightening the Score Matching Gap for Diffusion Models
Jul 5, 2026Benjamin Dupuis, Tyler Farghly, Maxime Haddouche +2Score-Based Diffusion Model Kullback-Leibler Divergence
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
Jul 1, 2026Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan WaniorekFourier Neural Operators Neural Operators
Operator Learning for Cubic Nonlinear Schrödinger Equation on Periodic Domains
Jun 25, 2026Emmanuel E. Oguadimma, Victory C. Obieke, Xueying YuFourier Neural Operators Logarithmic Sobolev Inequalities
Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Jun 16, 2026Yahong Yang, Zecheng Zhang, Wei Zhu +2Logarithmic Sobolev Inequalities Probabilistic Operator Learning
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
Jun 15, 2026Baicheng Li, Haizhao Yang, Shijun ZhangNeural-Network Approximation Logarithmic Sobolev Inequalities
Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks
May 29, 2026Yunfei Yang, Jun FanLogarithmic Sobolev Inequalities Neural-Network Approximation
Random Neural Network Expressivity for Non-Linear Partial Differential Equations
May 24, 2026Muhammed Ali Mehmood, Lukas GononPartial Differential Equations Neural-Network Approximation
Coloring the Noise: Adversarial Sobolev Alignment for Faithful Image Super Resolution
May 22, 2026Hongbo Wang, Huaibo Huang, Pin Wang +3Generative Super-Resolution Large-Scale Image Generation
Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
May 21, 2026Margalit Glasgow, Joan BrunaTwo-Layer Neural Networks Wasserstein Gradient Flows
Shallow ReLU $^s$ Networks in $L^p$ -Type and Sobolev Spaces: Approximation and Path-Norm Controlled GeneralizationShallow ReLU^s Networks in L^p-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization
May 18, 2026Weizhao Li, Fanghui Liu, Lei ShiLogarithmic Sobolev Inequalities Rectified Linear Unit Networks
Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process
May 18, 2026Yuta KoikeWasserstein Distance Logarithmic Sobolev Inequalities
Universal Approximation of Nonlinear Operators and Their Derivatives
May 14, 2026Filippo de FeoProbabilistic Operator Learning Logarithmic Sobolev Inequalities
A proximal gradient algorithm for composite log-concave sampling
May 12, 2026Linghai Liu, Sinho ChewiNon-Log-Concave Proximal Gradient Descent
Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces
May 12, 2026Jeunghun Oh, Kyeongwon Lee, Jaeyong Lee +1Kolmogorov-Arnold Networks Bayesian Neural Networks
Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems
May 5, 2026Hanfei Zhou, Lei ShiBoundary Value Problems Logarithmic Sobolev Inequalities
Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networksRandom test functions, H^{-1} norm equivalence, and stochastic variational physics-informed neural networks
May 5, 2026Diego MarcondesPartial Differential Equation Benchmarks Logarithmic Sobolev Inequalities
Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
May 4, 2026Nicole HaoLogarithmic Sobolev Inequalities Fourier Neural Operators
Structured Approximations of Measures
Oct 13, 2023Keaton Hamm, Varun KhuranaProbability Measures Wasserstein Distance

Sep 17, 2026 · stat.MLJ/K move · Enter open · S save

Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks

Xianjun Li, Yunfei Yang

Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights. We extend these results from uniform approximation to approximation in Sobolev norm. Specifically, we analyze how well Sobolev functions in

W^{n,p}

can be approximated by neural networks with width

W

, depth

L

and path norm bounded by

K

, when the approximation error is measured in the

W^{1,p}

-norm. For shallow networks with depth

L=1

, we derive the approximation error bound

\mathcal{O}(\max\{W^{-(n-1)/d}, K^{-(n-1)/(s-n)}\})

, when the smoothness index satisfies

n<s=(d+3)/2

and the input is

d

-dimensional. For deep networks, we remove the restriction on the smoothness by showing that the approximation bound

\mathcal{O}(K^{-(n-1)/(d+d/p+1)})

holds if the width

W

and depth

L

are sufficiently large.

Logarithmic Sobolev Inequalities Rectified Linear Unit Networks Neural-Network Approximation Approximation Generalization Bounds Neural Network

Open paper Ask about it PDF