neuralnet() — Neural networks

Stacks simple bending units into a flexible function.

neuralnet(hidden_units, X, y)

Key idea

• A hidden unit is a tiny building block that makes one smooth bend; summing many of them builds a flexible curve. (e.g. 8 units -> 8 bends added up)
• The weights (numbers scaling each input) are learned by gradient descent using backpropagation.
• More units or layers = more flexibility and more risk of overfitting (memorising noise).
• With enough hidden units a network can approximate almost any shape.

Definition

$$\hat{y}={\sum }_h{w}_h\tanh (a_h+b_{h}x)+w_0$$

$h$

a hidden unit

$\tanh$

the activation that bends the input

$w_h,b_h$

weights learned by gradient descent

In plain words

Take a bunch of simple curved building blocks, slide and stretch each one, and stack them until they trace any shape you like.

Where you'd use it

• Image, speech, and text tasks where features interact in complex ways.
• Any rich, large dataset where flexible non-linear models shine.
• The foundation of modern deep learning and large language models.

Frequently asked questions

Do I need to scale the inputs?

Yes — and you usually need plenty of data; small sets overfit badly.