Forward Propagation: Following the Calculation

Audience

ages 10–15

Duration

30 to 40 min

Adventure

3/8

Badge to earn

Propagation Tracer

Today's mission

Trace a prediction from input to logits while keeping every intermediate value.

Proof of success: explain "Forward propagation: following the calculation", complete "The Operations Relay" and name the limit of the analogy.

The story

Mehdi receives a card [2, 1] and a small already-tuned network. He computes the first layer, applies ReLU, then computes two logits. Instead of writing down only the final category, he keeps a trail of every number. When a classmate finds another answer, they pinpoint a forgotten addition in the hidden layer. Forward propagation is not an opinion: it is the orderly execution of the model's operations.

What is technically true

Watch the mechanism, not just the result. The three markers below let you check each step. Here, your anchor is "Forward propagation: following the calculation".

• Forward propagation uses the current parameters without changing them: input → transformations → output.
• A computation graph keeps the dependencies between operations; it will later be used to compute the gradients.
• During inference we also do a forward pass, but without backpropagation and without updating the weights.

The vertical map

The map is an audit trail: each intermediate result must match the operation right before it. Read the diagram from top to bottom: each arrow announces a transformation or a check, never a thought inside the machine.

A useful analogy — and where it breaks

The analogy: It's a marble's path through a transparent machine where each station records its transformation.

Where it breaks: A real network processes many examples in parallel as tensors, and some layers behave differently between training and evaluation. An analogy helps you get started; it never replaces the data, the calculations or a test.

Screen-free activity — The Operations Relay

Materials: six station cards, an input [2, 1], simple weights and a trace sheet
Suggested time: 10 to 20 minutes.

1. Line up input, dense layer, bias, ReLU, output layer and logits.
2. At each station, perform only the written operation and note the received value and the transmitted value.
3. Swap two stations and check whether the result changes or becomes impossible.
4. Ask another person to redo the trace without seeing your final answer.

What you should notice: the order and the intermediate values make a prediction reproducible and an error locatable.

Optional challenge

Add a batch of two inputs. Give the shape at each station without computing all the numbers.

Safety, fairness and human choice

A reproducible output can still be harmful if the inputs are poorly chosen. Checking the calculation does not replace evaluating the use.

Responsible question: Who should be allowed to inspect the trace when a prediction affects a person?

Mini-quiz with answers

1. Do the weights change during forward propagation?

   Answer: No. They are used in the calculation but are not updated at this step.

2. What is an intermediate value used for?

   Answer: To continue the calculation, check shapes and locate the origin of an error.

3. Do inference and training have the same purpose?

   Answer: No. Inference produces an output; training continues with loss, gradients and updates.

Competency badge

Propagation Tracer — You earn this badge if you can explain the diagram without reading, show the result of the activity and kindly correct a wrong answer.