More neurons in the hidden layer than predictive features in neural nets

This week, we were talking about neural networks for the first time, and I was saying that, in many illustrations of neural networks, there was a layer with fewer neurons than predictive variables, but sometimes, it could make sense to have more neurons in the layer than predictive variables, To illustrate, consider a simple example with one single variable [latex]x[/latex], and a binary outcome [latex]y\\in\\{0,1\\}[/latex] set.seed(12345) n = 100 x = c(runif(n),1+runif(n),2+runif(n)) y = rep(...