Universal Consistency of Wide and Deep ReLU Neural Networks and Minimax Optimal Convergence Rates for Kolmogorov-Donoho Optimal Function Classes

Hyunouk Ko, Xiaoming Huo
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:24859-24871, 2024.

Abstract

In this paper, we prove the universal consistency of wide and deep ReLU neural network classifiers. We also give sufficient conditions for a class of probability measures for which classifiers based on neural networks achieve minimax optimal rates of convergence. The result applies to a wide range of known function classes. In particular, while most previous works impose explicit smoothness assumptions on the regression function, our framework encompasses more general settings. The proposed neural networks are either the minimizers of the $0$-$1$ loss that exhibit a benign overfitting behavior.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-ko24b, title = {Universal Consistency of Wide and Deep {R}e{LU} Neural Networks and Minimax Optimal Convergence Rates for Kolmogorov-Donoho Optimal Function Classes}, author = {Ko, Hyunouk and Huo, Xiaoming}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {24859--24871}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/ko24b/ko24b.pdf}, url = {https://proceedings.mlr.press/v235/ko24b.html}, abstract = {In this paper, we prove the universal consistency of wide and deep ReLU neural network classifiers. We also give sufficient conditions for a class of probability measures for which classifiers based on neural networks achieve minimax optimal rates of convergence. The result applies to a wide range of known function classes. In particular, while most previous works impose explicit smoothness assumptions on the regression function, our framework encompasses more general settings. The proposed neural networks are either the minimizers of the $0$-$1$ loss that exhibit a benign overfitting behavior.} }
Endnote
%0 Conference Paper %T Universal Consistency of Wide and Deep ReLU Neural Networks and Minimax Optimal Convergence Rates for Kolmogorov-Donoho Optimal Function Classes %A Hyunouk Ko %A Xiaoming Huo %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-ko24b %I PMLR %P 24859--24871 %U https://proceedings.mlr.press/v235/ko24b.html %V 235 %X In this paper, we prove the universal consistency of wide and deep ReLU neural network classifiers. We also give sufficient conditions for a class of probability measures for which classifiers based on neural networks achieve minimax optimal rates of convergence. The result applies to a wide range of known function classes. In particular, while most previous works impose explicit smoothness assumptions on the regression function, our framework encompasses more general settings. The proposed neural networks are either the minimizers of the $0$-$1$ loss that exhibit a benign overfitting behavior.
APA
Ko, H. & Huo, X.. (2024). Universal Consistency of Wide and Deep ReLU Neural Networks and Minimax Optimal Convergence Rates for Kolmogorov-Donoho Optimal Function Classes. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:24859-24871 Available from https://proceedings.mlr.press/v235/ko24b.html.

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