exercises.md

Neuron Exercises

Exercise 1: Label the factory

For each room in the tiny-factory metaphor, name:

1. the input it receives
2. the output it produces
3. the mathematical symbol for that output

Exercise 2: One forward pass by hand

Given:

$$x_1 = 1,\quad x_2 = 0,\quad w_1 = 0.8,\quad w_2 = -0.4,\quad b = 0.1$$

1. Compute z
2. Compute \hat{y} = \sigma(z)
3. If the target is y = 1, compute the squared-error loss

Exercise 3: Read the dependency chain

Write the parameter-to-loss path for:

1. w1
2. w2
3. b

using words, not only symbols.

Exercise 4: Explain the local derivatives

Why are these true?

$$\frac{dz}{dw_1} = x_1,\quad \frac{dz}{dw_2} = x_2,\quad \frac{dz}{db} = 1$$

Use both:

• one algebra sentence
• one metaphor sentence

Exercise 5: Read the update rule in English

Explain this in one plain sentence:

$$w := w - \eta \frac{dL}{dw}$$

Exercise 6: Memory hook

Without looking back, write the two three-word summaries for:

1. forward pass
2. backward pass

Exercise 7: Run the executable ladder

Run these examples in order:

cargo run --manifest-path code/Cargo.toml -p rust_ml_neuron --example 01_weighted_sum
cargo run --manifest-path code/Cargo.toml -p rust_ml_neuron --example 02_forward_pass
cargo run --manifest-path code/Cargo.toml -p rust_ml_neuron --example 03_one_step_training

For each example, write one sentence that connects the printed numbers to the lesson vocabulary.

Failure Signals

• You can compute z but cannot explain why the sigmoid map comes next.
• You describe the backward pass as "magic correction" instead of tracing loss back to each parameter.
• You mix up Prediction, Target, Loss, Gradient, and Adjustment as if they were the same kind of number.
• You run the examples but cannot connect the printed values to the type names in code/neuron.

Debugging Hints

• Draw the forward path first: FeatureVector -> WeightedSum -> Prediction -> Loss.
• For each parameter, ask which intermediate value it directly changes.
• Keep the three-word hooks nearby: forward is mix, squash, judge; backward is blame, trace, adjust.
• When an example prints a value, write the Rust newtype name beside the printed number.