Learning Korobov Functions by Correntropy and Convolutional Neural Networks

Zhiying Fang*, Tong Mao, Jun Fan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


Combining information-theoretic learning with deep learning has gained significant attention in recent years, as it offers a promising approach to tackle the challenges posed by big data. However, the theoretical understanding of convolutional structures, which are vital to many structured deep learning models, remains incomplete. To partially bridge this gap, this letter aims to develop generalization analysis for deep convolutional neural network (CNN) algorithms using learning theory. Specifically, we focus on investigating robust regression using correntropy-induced loss functions derived from information-theoretic learning. Our analysis demonstrates an explicit convergence rate for deep CNN-based robust regression algorithms when the target function resides in the Korobov space. This study sheds light on the theoretical underpinnings of CNNs and provides a framework for understanding their performance and limitations.

Original languageEnglish
Pages (from-to)718-743
Number of pages26
JournalNeural Computation
Issue number4
Early online date21 Mar 2024
Publication statusPublished - Apr 2024

Scopus Subject Areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience


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