mlsanityData to 14 Oct 2026

Universal Consistency of Deep Convolutional Neural Networks

arXiv 2106.12498 ↗First posted 23 Jun 2021cs.LG cs.IT math.ITcited by 16

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Abstract (arXiv)

Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this paper, we prove that implementing empirical risk minimization on DCNNs with expansive convolution (with zero-padding) is strongly universally consistent. Motivated by the universal consistency, we conduct a series of experiments to show that without any fully connected layers, DCNNs with expansive convolution perform not worse than the widely used deep neural networks with hybrid structure containing contracting (without zero-padding) convolution layers and several fully connected layers.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 12 of its 28 references that are in the map. First posted on arXiv 23 Jun 2021.

Builds on

12 of 28 references.

References · 12

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  3. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 466
  4. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  5. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 311
  6. 2018Universality of Deep Convolutional Neural Networkscited by 176
  7. 2017Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activationscited by 104
  8. 2018ECG Heartbeat Classification: A Deep Transferable Representationcited by 76
  9. 2019Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networkscited by 40
  10. 2018Generalization and Expressivity for Deep Netscited by 11
  11. 2019Realization of spatial sparseness by deep ReLU nets with massive datacited by 10
  12. 2019Realizing data features by deep netscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 4; 2024: 3; 2025: 2; 2026: 1.

16 papers.

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  1. 2022Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networkscited by 21
  2. 2021Approximation Properties of Deep ReLU CNNscited by 15
  3. 2023Optimal rates of approximation by shallow ReLUk neural networks and applications to nonparametric regressioncited by 15
  4. 2024On the rates of convergence for learning with convolutional neural networkscited by 10
  5. 2022Learning Ability of Interpolating Deep Convolutional Neural Networkscited by 9
  6. 2023Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learningcited by 4
  7. 2024Generalization Analysis of Online Stochastic Gradient Descent for Overparameterized Two-Layer Neural Networkscited by 4
  8. 2025Higher Order Approximation Rates for ReLU CNNs in Korobov Spacescited by 4
  9. 2022Deep Learning is Provably Robust to Symmetric Label Noisecited by 2
  10. 2022Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functionscited by 1
  11. 2022Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantificationcited by 1
  12. 2023On the Connection between Lp and Risk Consistency and its Implications on Regularized Kernel Methodscited by 1
4 more
  1. 2023Optimal Approximation and Learning Rates for Deep Convolutional Neural Networkscited by 1
  2. 2024Component-based Sketching for Deep ReLU Netscited by 1
  3. 2025Transformers Are Universally Consistentcited by 0
  4. 2026Ratio-based Loss Functionscited by 0