Convergence rates of deep ReLU networks for multiclass classification

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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.
Original languageEnglish
Pages (from-to)2724 - 2773
Number of pages50
JournalElectronic Journal of Statistics
Issue number1
Publication statusPublished - 2022


  • conditional class probabilities
  • Convergence rates
  • margin condition
  • multiclass classification
  • ReLu networks


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