Skip to content
Optimal Lab

AI Engineering · interactive

What a model is

A model is a function with knobs: an input goes in, a prediction comes out, and the knobs, the parameters, decide which. Training is letting the data set the knobs. Fit a delivery-time model by hand, then let the data do it, and see what each shape says about an order it has never seen.

A line · time = a + b × km

off by 6.3 min

05010005101520km

Dots: past orders, in minutes. Line: what the model predicts at every distance. Hollow: the new orders at 7.5 and 20 km.

Off by 6.3 minutes per order. Drag the parameters in step 3, or press Fit in step 4.

Model shape

1

Collect examples

Inputs with the answers you want. Here: how far an order went, and how long it took.

1 km → 14 min · 2 km → 19 min · 3 km → 21 min · 4 km → 27 min · 5 km → 29 min · 6 km → 35 min · 7 km → 38 min · 8 km → 41 min · 9 km → 47 min · 10 km → 49 min · 11 km → 55 min · 12 km → 57 min

2

Choose a shape

The shape fixes the kind of answer the model can give and how many parameters it has. The data can only tune the parameters, not change the shape.

time = a + b × km

2 parameters: a and b.

3

Set the parameters

Every setting is a different model. Drag them and watch the predictions and the error move.

average error: 6.33 min

4

Let the data set them

Training searches for the parameters with the smallest error on the examples. For a line that's one formula; for a neural network it's gradient descent, one small nudge at a time.

best: a = 10.27, b = 3.96 · error 0.83 min

5

Predict for an input it never saw

The point of a model is the next order, not the old ones. A shape with the right idea in it (time grows with distance) can answer beyond its examples; a table can only repeat them.

  • 7.5 km → 35 min
  • 20 km → 60 min

How many parameters

  • This line2
  • This curve3
  • The XOR network (neural-networks session)9
  • GPT-2 small124 million
  • Llama 3.3 70B70.6 billion

An LLM is the same idea: a fixed shape (the transformer) with billions of knobs, set by the data.

In production

Tools and technologies

Every library fits parameters to data; the shapes range from a line to a transformer.

Not tied to one language — use these names when you search docs or design a system.