mlsanityData to 14 Oct 2026

Analysis of convolutional neural network image classifiers in a rotationally symmetric model

arXiv 2205.05500 ↗First posted 11 May 2022stat.ML cs.LGcited by 4

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Abstract (arXiv)

Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Here we consider images as random variables with values in some functional space, where we only observe discrete samples as function values on some finite grid. Under suitable structural and smoothness assumptions on the functional a posteriori probability, which includes some kind of symmetry against rotation of subparts of the input image, it is shown that least squares plug-in classifiers based on convolutional neural networks are able to circumvent the curse of dimensionality in binary image classification if we neglect a resolution-dependent error term. The finite sample size behavior of the classifier is analyzed by applying it to simulated and real data.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 25 of its 46 references that are in the map. First posted on arXiv 11 May 2022.

Builds on

25 of 46 references.

References · 25

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13 more
  1. 2019Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov spacecited by 46
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 2.

4 papers.

  1. 2026Learning Sparse Compositional Functions with Norm-Constrained Neural Networkscited by 3
  2. 2024On the VC dimension of deep group convolutional neural networkscited by 1
  3. 2024Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descentcited by 0
  4. 2026Press Start to Charge: Videogaming the Online Centralized Charging Scheduling Problemcited by 0