The Double Descent Behavior in Two Layer Neural Network for Binary Classification

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.