Grades 9–12

Forward, Backward, Update

The three steps every modern AI repeats billions of times as it trains.

How did AI get so good?

Every AI tool you used this week was trained the same way: three steps, repeated billions of times.

1

Forward pass

Push the inputs through the network to make a prediction.

2

Back propagation

Measure the error and send it back through the network.

3

Weight update

Nudge every weight to make the next error smaller.

Today you'll do all three by hand.

High School · Grades 9–12

Key vocabulary

Hidden layer
Nodes between the inputs and the outputs. Their values are worked out, never given.
Weighted sum
Each value coming into a node times its connection's weight, added together.
Forward pass
Working out every node's value, layer by layer, from inputs to outputs.
Error
The output value minus the target value.
Back propagation
Sending the error back across each weight, so every node knows its share of the mistake.
Learning rate
A small number that sets how big each weight update is.
Gradient descent
Training by moving every weight a small step in the direction that makes the error smaller.

High School · Grades 9–12

Step 1

Forward through the middle

The Talent Show Predictor Forward Propagation tab ↗

Each node works out a weighted sum: each input times its weight, added together. Predict each middle node, then the output.

top: 2 × 1 + 3 × 2 = ?8
bottom: 2 × 2 + 3 × 1 = ?7
audience: 8 × 5 + 7 × 10 = ?110
1221510 2 acts 3 posters ?8 ?7 ?110 audience

High School · Grades 9–12

Step 2

Send the error back

The Street Musician Predictor Back Propagation tab ↗

The network predicts $20. The musician really collected $23.

error = output - target

output: 20 - 23 = ?-3
middle: -3 × 0.5 = ?-1.5

The input values never receive an error, because nothing can change them.

10200.5 2 morning hrs 1 evening hrs 40 error -1.5 20 dollarserror -3

High School · Grades 9–12

Step 3

Update a weight

The Recycling Drive Predictor Weight & Bias Update tab ↗

2 classes take part. The network predicts 3 bags of cans, but the target is 6. The learning rate is 0.02.

output error: 3 - 6 = ?-3
middle errors: -3 × 1 and -3 × 0.5 = ?-3 and -1.5
adjustment = input × error × learning rate = 2 × -3 × 0.02 = ?-0.12
new weight = weight - adjustment = 1 - (-0.12) = ?1.12

High School · Grades 9–12

Finished early?

Find the learning rate

The Test Score Predictor 02 Weight & Bias Update tab ↗

At a learning rate of 0.2, this network's weights blow up.

  1. Watch it train at 0.2. What goes wrong?
  2. Try the other learning rates, and record what each one does.
  3. Find the one that settles.

What goes wrong above it? And below it?

High School · Grades 9–12

Discussion

  1. Why does the error travel back across the weights, rather than straight to every node?
  2. Why is the adjustment subtracted?
  3. What went wrong with a learning rate of 0.2?
  4. Large AI models have billions of weights. What changes, and what stays the same?

High School · Grades 9–12

Exit ticket

A weight of 4 connects an input of 3 to an output with a target of 10. The learning rate is 0.1.

  1. What is the output?
  2. What is the error?
  3. What is the adjustment?
  4. What is the new weight?

High School · Grades 9–12

Same three steps, billions of weights

The AI tools you use were trained by these same three steps, forward, backward, update, on far more data.

The scale changes. The arithmetic doesn't.

Keep exploring at iinnoo.app

High School · Grades 9–12