Model as a Function

A function maps inputs to outputs.

A model does the same thing, but with stored parameters:

y_hat = f(x; theta)

Read this as:

prediction = model(input; parameters)

The semicolon is a convention. It separates the input x from the parameters theta.

The input is what the model is asked about. The parameters define which function the model currently represents.

Same input, different parameters

Let:

f(x; w, b) = wx + b

For the same input x = 2:

w = 3, b = 1   -> f(2) = 7
w = 1, b = 5   -> f(2) = 7
w = 4, b = 0   -> f(2) = 8

Changing parameters changes the function.

Training is the process of finding parameters that make the model's outputs useful for the task.