Parameters and model size

Year 8 · Lesson 2 · Content 2026.11.02.1

All supplied-record lessons · Open interactive lesson

Supplied-record alternative. Enter your responses in your school assignment. These supplied results support learning but do not show that you ran an algorithm.

Your goal

Choose a model using tested results, speed and cost rather than size alone.

To be able to use evidence to explain a trade off between model size and useful performance.

Before you start

A single output has two input weights and one added number. How many settings?

Choices: 3 / 1 / 2

Bridge feedback after trying

Two weights plus one added number gives three settings. One node can use several settings.

Words for this lesson

Parameter: A numerical setting learned during training.
Weight: A parameter that changes a connection's influence.
Trade off: A choice where a gain can come with a cost.

The idea

Weights and biases are parameters. A node can use several of them. A larger model may represent more complex patterns but can require more memory or calculation. More settings do not guarantee better performance on a particular task. Compare suitable tests, response time and costs against what the user actually needs.

A completed example

Practice network: three inputs connect to one output with one bias. Count three weights plus one bias, giving four parameters. The input nodes have no biases in this specified example.

Check your understanding

One node may have ...

Several parameters
Exactly one parameter always
No calculation

Practice feedback after trying

Several parameters. Weights and a bias are different settings.

Which supplied model meets both constraints?

Small
Larger
Neither

Practice feedback after trying

Small. 92/100 and 40 ms meet the two stated conditions.

Task 1 · Make a prediction

Two hidden nodes mean two parameters

Options: Yes / No / Not sure

Write your prediction, or state that you skipped it.

Try it using supplied records

Predict whether two hidden nodes mean two parameters.
Select the Small network. Reveal each family of connections or biases and enter its count.
Select Larger and count using the same rules. Use Count with me to highlight one setting at a time if needed.
Compare the complete totals and make a prediction about whether the larger service must be the best choice.

Manual parameter counts · supplied service results

Complete data and source records

Specified networks. Fictional teaching data.
Network	Inputs	Hidden nodes	Outputs	Bias rule
Small	2	2	1	One per hidden and output node, none on inputs
Larger	2	4	1	One per hidden and output node, none on inputs

Read as stacked records

Network: Small
Inputs: 2
Hidden nodes: 2
Outputs: 1
Bias rule: One per hidden and output node, none on inputs

Network: Larger
Inputs: 2
Hidden nodes: 4
Outputs: 1
Bias rule: One per hidden and output node, none on inputs

Fictional same-hardware local results. Fictional teaching data.
Model	Correct out of 100	Median response in ms	AED per 1000 requests
Small	92	40	0.02
Larger	94	300	0.1

Read as stacked records

Model: Small
Correct out of 100: 92
Median response in ms: 40
AED per 1000 requests: 0.02

Model: Larger
Correct out of 100: 94
Median response in ms: 300
AED per 1000 requests: 0.1

Expected results · supplied

These are supplied reference results. They are separate from your own explanation. No code needs to run to read them.

1. Fully connected layers only. For h hidden nodes: input weights=2h; hidden biases=h; output weights=h; output bias=1; total=4h+1. h=2 gives 4+2+2+1=9; h=4 gives 8+4+4+1=17.

2. Small meets correctness and latency conditions. Larger meets correctness but fails median response below 100 ms. Small is cheaper in the supplied fictional prices. No energy values can be inferred from these prices.

3. Controls select only Small or Larger; no training, learning-rate or layer editor. Count reveal has text equivalent 4 connections etc. Preserve first count attempts and help used separately.

Help with this step

Hint 1

Count connections, not just the circles.

Hint 2

Every hidden and output node adds one bias under this task's rules. Input nodes add none.

Hint 3

Practice: 2 inputs to one output give 2 weights plus 1 bias, or 3 parameters. Now count your hidden layer separately.

Task 2 · Use the evidence

Check each model against the school brief: at least 90 correct of 100 and median response below 100 milliseconds.
Recommend a model using one performance result and one constraint.
Name missing evidence and explain why this small table does not show that larger models always lose or always win.

My explanation

Write in your school assignment. Keep these answers in your own words.

Network Small

Input weights (settings)
Hidden biases (settings)
Output weights (settings)
Output bias (settings)
Total (settings)

Network Larger

Input weights (settings)
Hidden biases (settings)
Output weights (settings)
Output bias (settings)
Total (settings)

Model Small

Meets correctness requirement: Yes / No / Not yet established
Meets time limit: Yes / No / Not yet established

Model Larger

Meets correctness requirement: Yes / No / Not yet established
Meets time limit: Yes / No / Not yet established

Your decision

My choice and two evidence details
Missing evidence

Explain a fresh example

The larger model gets two extra requests correct but takes 300 ms. The brief requires below 100 ms. Give a decision and one limit on the evidence.

My confidence

I need another explanation / I can explain with help / I can explain with my own example

My next step

Write what you will do next.

Optional depth

Calculate the supplied running price for 10000 requests. Why does use still have costs after training is finished?

What this activity can show

Networks are countable diagrams; the site does not train these networks. Service results are supplied fictional records and are not derived from parameter counts.

This is a student learning record. Submission is completed through the school assignment system.