mlsanityData to 14 Oct 2026

A Quantitative Functional Central Limit Theorem for Shallow Neural Networks

arXiv 2306.16932 ↗First posted 29 Jun 2023math.PR stat.MLcited by 8

Not on the map. Why?

Abstract (arXiv)

We prove a Quantitative Functional Central Limit Theorem for one-hidden-layer neural networks with generic activation function. The rates of convergence that we establish depend heavily on the smoothness of the activation function, and they range from logarithmic in non-differentiable cases such as the Relu to √n for very regular activations. Our main tools are functional versions of the Stein-Malliavin approach; in particular, we exploit heavily a quantitative functional central limit theorem which has been recently established by Bourguin and Campese (2020).

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 13 of its 30 references that are in the map. First posted on arXiv 29 Jun 2023.

Builds on

13 of 30 references.

References · 13

  1. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 927
  2. 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 331
  3. 2021The Principles of Deep Learning Theorycited by 173
  4. 2016Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivitycited by 138
  5. 2020Deep Equals Shallow for ReLU Networks in Kernel Regimescited by 85
  6. 2019Non-Gaussian processes and neural networks at finite widthscited by 78
  7. 2021Random Neural Networks in the Infinite Width Limit as Gaussian Processescited by 44
  8. 2019Time/Accuracy Tradeoffs for Learning a ReLU with respect to Gaussian Marginalscited by 32
  9. 2022Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networkscited by 25
  10. 2020Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernelscited by 19
  11. 2021Non-asymptotic approximations of neural networks by Gaussian processescited by 19
  12. 2021Rate of Convergence of Polynomial Networks to Gaussian Processescited by 13
1 more
  1. 2023Non-asymptotic approximations of Gaussian neural networks via second-order Poincar'e inequalitiescited by 11

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 3; 2026: 1.

8 papers.

  1. 2023Quantitative CLTs in Deep Neural Networkscited by 20
  2. 2023Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processescited by 13
  3. 2025Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weightscited by 5
  4. 2024Spectral complexity of deep neural networkscited by 3
  5. 2024Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selectioncited by 3
  6. 2025Fractal and Regular Geometry of Deep Neural Networkscited by 1
  7. 2026Quantitative Gaussian-Process limits of Tensor Programscited by 1
  8. 2025Critical Points of Random Neural Networkscited by 0