The question was “In an A.I. model, what exactly is a ‘parameter’ counting?”

Most machine-learned models have two aspects:

1) a structure into which numbers are plugged to define the model,
2) the numbers themselves, which are learned (or adjusted, or tweaked) based on training data

The numbers in (2) are called the “parameters”, and sometimes people describe the complexity of a model by saying how many parameters it has.

The simplest example of a model is a equation of a line that you might draw on a 2D graph:

y = mx + b

The letters here correspond to the following things:

• ‘x’ is the number that is the input to the model
• ‘y’ is the output of the model, or the number that it predicts
• ‘m’ is the slope of the line
• ‘b’ is the y-intercept of the line, controlling how far above or below the x-axis the line is when x=0

In this example, the equation itself is the structure (y = mx + b), and the parameters are ‘m’ and ‘b’. Before you can use this equation to predict y from a given x, you need to decide the values of ‘m’ and ‘b’. One way to do this is to learn the right values by looking at a lot of x-y pairs, and choosing the ‘m’ and ‘b’ that make the overall error in your prediction of ‘y’ as small as possible.

Given this structure you could apply it to different problems with their own datasets, and you’ll learn different values of ‘m’ and ‘b’. For example, given heights and weights of a lot of different people, you could learn the right ‘m’ and ‘b’ to predict weight from height. Given pairs of floor-plan area and home sale price, you can learn to predict sale price from area.

This kind of model is very simple, and has only two parameters. Fancier models like deep neural nets can have hundreds or thousands or millions of parameters. As a general rule, the more parameters a model has, the more data you will need to train it.