Follow an update pipeline
Read products, sums, gates, and ordering as a sequence of operations.
Course lessons · 4 of 5
Calculate a composed update and explain why operation order matters.
Useful background: Normalization changes comparisons
A pipeline has intermediate states
The G16 source combines family transformations, blending, stability gating, and normalization. These stages are separate functions with intermediate outputs. To understand the whole update, trace a small input through each stage and keep the intermediate values.
Composition is often order-sensitive. Scaling an input and then adding a bias generally differs from adding the bias first and then scaling. Matching family names across two source versions therefore does not establish that their trajectories are equal.
Products create gates; sums mix contributions
A product becomes zero if any factor is zero. In a teaching learning-drive expression, multiplying activation, plasticity, and confidence makes each factor a gate on the final magnitude. The source must still define the allowed range and meaning of each factor.
A weighted sum combines contributions, and weights summing to one form an average when the relevant conditions hold. Its result should be inspected before later clipping or normalization, because those stages can hide large intermediate values.
Compare two operation orders
1Define both operations
Let f(x) = x + 1 and g(x) = 2x. These simple teaching functions isolate the effect of order.
2Apply addition before scaling
Starting at x = 3 gives four, then eight.
3Reverse the order
Scaling first gives six, then seven. The functions are the same; their composition differs.
Make the idea respond
This laboratory implements the weighted-sum part of a composed calculation. Keep the values fixed and change one weight to see its normalized contribution change. It does not automatically compose f(x) = x + 1 with g(x) = 2x or compute the three-factor learning-drive product; those operations are worked separately above.
Change one input at a time. Predict what should happen, then compare the computed result with your prediction.
Teaching model · computed in your browser
Build a weighted score
Change component values and weights. Watch normalization turn them into a single, explainable score.
vᵢ is a component value from 0 to 1; wᵢ is a nonnegative raw weight. Divide every weight by their positive total before combining the values. These illustrative values are not measurements from a live AI system.
Try this: double all three weights. The normalized weights and total score should stay the same. Then set all weights to zero.
The default worked example is shown below.
Normalize before adding: divide each raw weight by 6. Then S = 0.4 + 0.2 + 0.0667 = 0.6667. Multiplying every raw weight by the same positive factor leaves the result unchanged. Choosing weights expresses a modeling decision; it does not validate what a score means.
| Component | Value | Raw weight | Normalized weight | Contribution |
|---|---|---|---|---|
| Component A | 0.8 | 3 | 0.5 | 0.4 |
| Component B | 0.6 | 2 | 0.3333 | 0.2 |
| Component C | 0.4 | 1 | 0.1667 | 0.0667 |
Your turn.
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Use these questions when studying without interactive controls. Opening a written solution does not earn progress.
With f(x) = x + 1 and g(x) = 2x, what is g(f(4))?
Read the solution
The result is 2 × (4 + 1) = 10.
A teaching drive is activation × plasticity × confidence = 0.8 × 0.5 × 0.25. What is the drive?
Read the solution
0.4 × 0.25 = 0.1.
If one factor in that product is zero, what happens?
- The result becomes undefined.
- The product is zero.
- The other factors are added instead.
- The product becomes one.
Read the solution
Multiplying by zero gives zero for these finite factors.
Two builds use the same family labels but apply gating and blending in different orders. What follows?
- Their trajectories require comparison; equality is not established.
- Their trajectories must be identical.
- Both implementations must be invalid.
- Their order can be ignored after naming the families.
Read the solution
Compare source-specific pipelines and outputs before claiming equivalence.
Follow the original record
Use the definitions you just practiced to read the project’s own notation, assumptions, and evidence.
The ideas to keep
- Keep intermediate states visible.
- Products can gate an update.
- Compare operation order across revisions.
Reading completion is separate from your practice evidence.
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