# Vanilla Neural Networks

> Source: <https://julin.ai/2026/08/28/vanilla-neural-networks/>
> Published: 2026-08-27 12:00:00+00:00

# Vanilla Neural Networks

A neural network is just a math function: `y = FNN(x)`

.

`FNN`

has a nested form. Think of it as a stack of layers. A 3-layer neural network that returns a scalar value looks like this:

`y = FNN(x) = f₃(f₂(f₁(x)))`

Each `f`

— `f₁`

, `f₂`

, … `fₙ`

— has the same form:

`f(x) = g(Wx + b)`

`W`

(the weight matrix) and `b`

(a bias vector) are the learned parameters, usually trained via gradient descent. `g`

is the activation function, and it can be chosen differently for each layer.