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Journal of Data Science


The Double Descent Behavior in Two Layer Neural Network for Binary Classification
Volume 23, Issue 2 (2025): Special Issue: the 2024 Symposium on Data Science and Statistics (SDSS), pp. 370–388
Pub. online: 1 April 2025      Type: Statistical Data Science      Open accessOpen Access
Received
1 October 2024
Accepted
6 March 2025
Published
1 April 2025

Abstract

Recent studies observed a surprising concept on model test error called the double descent phenomenon where the increasing model complexity decreases the test error first and then the error increases and decreases again. To observe this, we work on a two-layer neural network model with a ReLU activation function designed for binary classification under supervised learning. Our aim is to observe and investigate the mathematical theory behind the double descent behavior of model test error for varying model sizes. We quantify the model size by the ration of number of training samples to the dimension of the model. Due to the complexity of the empirical risk minimization procedure, we use the Convex Gaussian MinMax Theorem to find a suitable candidate for the global training loss.

Supplementary material

 Supplementary Material
We have included two supplementary files where Supplementary material 1 contains detailed calculations, theorems and proofs and Supplementary material 2 contains the R/RStudio codes used to draw the curves presented in the paper.

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Copyright
2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
generalization error model complexity over and under parameterization ReLU activation testing error

Funding
The research of Hailin Sang is partially supported by the Simons Foundation Grant 586789, USA.

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