Artificial neural networks with uniform norm-based loss functions-Reference-Cited by-同舟云学术

Artificial neural networks with uniform norm-based loss functions

Published:2024-04-23 Issue:3 Volume:50 Page:
ISSN:1019-7168
Container-title:Advances in Computational Mathematics
language:en
Short-container-title:Adv Comput Math

Author:

Peiris Vinesha,Roshchina Vera,Sukhorukova Nadezda

Abstract

AbstractWe explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network without hidden layers. We hypothesise that this may lead to superior classification results in some special cases where the training data are either very small or the class size is disproportional. Our numerical experiments performed on a simple artificial neural network with no hidden layer appear to confirm our hypothesis.

Funder

Australian research council

Deakin University

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s10444-024-10124-9.pdf

Reference24 articles.

1. Arnold, V.: On functions of three variables. Dokl. Akad. Nauk SSSR 114, 679–681,: English translation: Amer. Math. Soc. Transl. 28(1963), 51–54 (1957)

2. Bach, F., Jenatton, R., Mairal, J., Obozinski, G.: Convex optimization with sparsity-inducing norms, chap. 2, pp. 19–53. MIT press (2011)

3. Boyd, S., Vandenberghe, L.: Convex optimization, 7th (edn.) Cambridge University Press, New York, USA (2009)

4. Buolamwini, J., Gebru, T.: Gender shades: intersectional accuracy disparities in commercial gender classification. Proceedings of Machine Learning Research 81, 1–15 (2018)

5. Crouzeix, J.P.: Conditions for convexity of quasiconvex functions. Math. Oper. Res. 5(1), 120–125 (1980)