I get that activation functions are what introduces non-linearities into a neural network model. But what is confusing is that the parameters we are estimating are still linear. Neural networks seem to be, just a stacking of multiple Generalized Linear Models in that regard. Where each "activation function" is just the equivalent of a link function between our linear predictors and eventually the data.
Edit: The definition of linear I'm referring to is the one that GLMs appeal to which refers to its parameters (Weights) being linear. It was first stated by McCullagh and Nelder (1982) suggesting that the parameters affect the distribution of y only through linear combination: wx + b and then mapped to the data with a link function. (Introduction to GLMs, linear model and Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression?)
In the case of a Neural Network we are estimating linear parameters, and we are applying linear combinations with an activation or arguably equivalent "link function". So, unless somehow the composition of multiple GLMs stacked together doesn't qualify as a linear model anymore, it seems that this would make NN classify under a linear model category i.e. a stacking of multiple general linear models.