Each of these comes from a neural network. Let's find out what is at its core.

A zoo gets about 240 visitors for every hour of sunshine. How many on a day with 3 hours?

The 240 is the network's weight.

Neural network

A kind of AI that makes predictions by passing numbers along connections, multiplying and adding them.

Input value

The number that goes into the network, such as the hours of sunshine.

Weight

The number on a connection. The input is multiplied by it.

Output value

The number that comes out: the network's prediction.

Target output

The real answer. The output should match it.

The Zoo Visitors Predictor 02 Forward Propagation tab ↗

The network thinks each hour of sun brings 200 visitors. The targets say 240.

1. Click the weight and change it.
2. Step through all four inputs.
3. When an output matches its target, the lines turn green.

The Mountain Climb Calculator Forward Propagation tab ↗

The air gets 6 degrees colder for every kilometer you climb, so the weight is -6.

km climbed	1	2	3	4
change in degrees	?-6	?-12	?-18	?-24

What weight would you use for something that gets warmer as you climb?

For each network, list the inputs in one column and the outputs in the other.

Describe each pattern in words.

The zoo goes up by 240 each row. The mountain goes down by 6.

1. What does the sign of a weight tell you?
2. What would the mountain network say after 2.5 km?
3. What would a weight of 0 mean?

A bus costs $2.00 to board and $0.75 for each mile. A weight alone can't do it: the $2.00 is paid whatever the distance.

fare =	0.75	×	4 miles	+	2
y =	m	×	x	+	b
output =	weight	×	input	+	bias

Bias

A number added after multiplying, like the starting value b.

Slope

How much the output changes for each unit of input. In a network, the weight.

y-intercept

The output when the input is zero. In a network, the bias.

The Bus Fare Calculator 01 Forward Propagation tab ↗

Weight 0.75, bias 2. Predict each fare before you step to it.

miles	1	2	3	4
fare	?$2.75	?$3.50	?$4.25	?$5.00

What would a 0-mile ride cost? Why?

$2.00, the bias: the starting value.

Plot the four fares: miles on the x-axis, dollars on the y-axis. Draw the line through them.

1. Where does it cross the y-axis?
2. How much does it rise for each mile?

$2.00, the bias, and $0.75, the weight.

Invent a fare of your own, a taxi or a bike rental, with a starting price and a price per mile.

1. Write it as weight × input + bias.
2. Draw its line on the same grid as the bus.
3. Which is cheaper for a short ride? For a long one?

1. Where on the graph do you see the weight, and where the bias?
2. What happens to the line if the bias goes up by $1?
3. Where do two fares' lines cross, and what does that mean?

On a freezing day, weight × input + bias can give a negative number of ice creams.

An activation function fixes that: after the weight and the bias, it turns any negative value into zero.

Now a network can make a decision: switch an output off until something is true.

Activation function

A rule applied to a node's value. Here, it turns any negative value into zero.

Node

A circle in the network that holds a value. Each output is a node.

Threshold

The input where an output switches on, such as the temperature where sales begin.

The Ice Cream Sales Predictor Forward Propagation tab ↗

Weight 1, bias -60, and an activation function that turns any negative value into zero.

No one sells negative ice creams!

At what temperature do sales begin?

The Frost Warning Detector Forward Propagation tab ↗

This time, you set both the weight and the bias. The warning should grow as it gets colder, and switch off when it's warm.

1. As the temperature goes up, does the warning go up or down?
2. So is the weight positive or negative?
3. What bias makes the warning switch off at the right temperature?

The frost warning: weight -1, bias 4.

Sketch the frost warning's graph. Where is it flat?

1. Why does the frost warning need a negative weight?
2. What does the bias of 4 mean for the frost warning?
3. Where else might a network need to switch something off?

Real AI has millions of weights, so it has to find them by itself. First, it measures how wrong it is.

Error

The output value minus the target value: how far off the prediction is, and which way.

Positive error

The output is higher than the target: the network guessed too high.

Negative error

The output is lower than the target: the network guessed too low.

The Bean Plant Predictor Back Propagation tab ↗

The network guesses 3 cm a day. Watch the error for each plant.

plant	1	2	3	4
error	?1	?3	?2	?4

Every error is positive. What does that say about the weight?

The Arcade Ticket Predictor Back Propagation tab ↗

The weight is 3 tickets a coin. Predict each error before the network works it out.

round	1	2	3	4
error	?4	?3	?2	?6

Take turns: one predicts, the other checks.

1. Use the errors to choose a better weight for the bean plant.
2. Test it on paper against the four plants.
3. Add up the size of each error, ignoring the sign.

The smallest total wins. Can any weight make every error zero?

1. If every error is positive, should the weight go up or down?
2. Why can't any weight make every bean plant error zero?
3. Why ignore the sign when adding up the errors?

Yesterday you used the errors to choose a better weight. Today the network does it by itself.

Weight update

Changing a weight after an error, so the next error is smaller.

Learning

Updating the weights and bias, over and over, until the errors are small.

Training data

The inputs and targets the network learns from.

Testing data

Inputs and targets the network never learned from, to check whether it really learned.

The Delivery Time Predictor 01 Weight & Bias Update tab ↗

This network updates its own weight after every error. It starts at 0.5 minutes a kilometer.

Record the weight after every delivery. Where does it settle?

The Cookie Jar Predictor Weight & Bias Update tab ↗

The Cookie Jar Predictor learns its bias as well as its weight. The bias is the cookies in a fresh jar.

Record the bias every four jars. Which way is it heading?

The Tree Growth Predictor 02 Sample Networks tab ↗

This network learns its weight, from 1 to 1.27.

1. Train it on the training data.
2. Switch to the testing data: heights it has never seen.
3. Do its predictions still hold?

Done early? The Recycling Sorter learns to tell glass from plastic.

1. Why did the delivery weight never land exactly on 3?
2. Why test a network on data it never trained on?
3. What could go wrong if a network learned from bad data?

Write a network for something in your life with a weight and a bias. Draw it, graph it, and invent three targets that don't fit exactly.

Calculate the errors. Which way should the weight and bias be nudged?

Finish the sentence: "A neural network learns by…"