mlsanityData to 7 Oct 2026

Convergence rates of deep ReLU networks for multiclass classification

arXiv 2108.00969 ↗First posted 2 Aug 2021math.ST cs.LG stat.THcited by 21

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Abstract (arXiv)

For classification problems, trained deep neural networks return probabilities of class memberships. In this work we study convergence of the learned probabilities to the true conditional class probabilities. More specifically we consider sparse deep ReLU network reconstructions minimizing cross-entropy loss in the multiclass classification setup. Interesting phenomena occur when the class membership probabilities are close to zero. Convergence rates are derived that depend on the near-zero behaviour via a margin-type condition.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 7 of its 37 references that are in the map. First posted on arXiv 2 Aug 2021.

Builds on

7 of 37 references.

References · 7

  1. 2016End to End Learning for Self-Driving Carscited by 1,000
  2. 2016Error bounds for approximations with deep ReLU networkscited by 567
  3. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  4. 2018Fast convergence rates of deep neural networks for classificationcited by 46
  5. 2019On the rate of convergence of fully connected very deep neural network regression estimatescited by 14
  6. 2020On the rate of convergence of image classifiers based on convolutional neural networkscited by 7
  7. 2021Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networkscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 2; 2024: 5; 2025: 4; 2026: 4.

21 papers.

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  1. 2022Adaptive novelty detection with false discovery rate guaranteecited by 14
  2. 2022Automatic Change-Point Detection in Time Series via Deep Learningcited by 12
  3. 2024On the rates of convergence for learning with convolutional neural networkscited by 10
  4. 2024Misclassification bounds for PAC-Bayesian sparse deep learningcited by 7
  5. 2022Deep Neural Network Classifier for Multi-dimensional Functional Datacited by 5
  6. 2024How many samples are needed to train a deep neural network?cited by 5
  7. 2022Analysis of convolutional neural network image classifiers in a rotationally symmetric modelcited by 4
  8. 2023Classification of Data Generated by Gaussian Mixture Models Using Deep ReLU Networkscited by 4
  9. 2025Deep learning with missing datacited by 3
  10. 2025Dynamic Bundling with Large Language Models for Zero-Shot Inference on Text-Attributed Graphscited by 3
  11. 2026Sharper Generalization Bounds for Transformercited by 2
  12. 2022Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functionscited by 1
9 more
  1. 2023Multiclass classification for multidimensional functional data through deep neural networkscited by 1
  2. 2024Universal Consistency of Wide and Deep ReLU Neural Networks and Minimax Optimal Convergence Rates for Kolmogorov-Donoho Optimal Function Classescited by 1
  3. 2022Orthogonal Series Estimation for the Ratio of Conditional Expectation Functionscited by 0
  4. 2024Consistency for Large Neural Networks: Regression and Classificationcited by 0
  5. 2025A Two-Sample Test of Text Generation Similaritycited by 0
  6. 2025Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Conditioncited by 0
  7. 2026Plug-In Classification of Drift Functions in Diffusion Processes Using Neural Networkscited by 0
  8. 2026Adversarial Robustness of NTK Neural Networkscited by 0
  9. 2026Rate-optimal neural boundary detection from unlabeled noisy imagescited by 0