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Neural Networks

Teach the weight from one mistake

BOTIE

Calculate the derivative of half squared error for the supplied example.
Ready to test
0 passed · 0 failed · 1 not run

An empty floor. Start with the information your machine needs.

Received result

Your answer will arrive here.

Examples, experiments and workspace controls
Live values

Connect a tool's inputs to see what it produces. You can try a branch before connecting it to Result.

Try your own inputs

Use a copy of the example to try your own data. Keep the problem's assumptions in mind, and predict the effect of a change before checking the output. You can also add another branch to compare two ways of doing the calculation.

Start at an output arrow, then click or drag to an input. Drag empty space to pan. Delete removes a selection. Ctrl/Cmd+Z undoes a change.
Context for this challenge

Calculate the derivative of half squared error for the supplied example.

We now have the pieces needed to change a weight using an example. A single linear neuron makes a prediction, its label tells us the mistake, and the gradient tells us how the weight contributed. Let's connect those pieces into one learning step.

Inspect the component calculation
Multiply(
  Value: Subtract(
    Starting value: Multiply(
      Value: Training input
      Multiplier: Current weight
    )
    Value to remove: Training label
  )
  Multiplier: Training input
)
Examples and results
Training input
2
Current weight
1
Training label
5
Required result
-6
Try a fresh construction

This clears this draft, including its undo history. Earlier successful attempts stay recorded. Build again without opening hints to record an independent attempt.

Stuck? Inspect a worked construction

The tools below form one possible solution. You can assemble it, follow its signals, and undo that change to return to your own construction.

Assumptions and test precision

This is a small construction problem. The lesson explains the assumptions and the parts of the full method that this example leaves out. Numerical tests allow a difference of 0.001. Lists and structures must also have the right shape.

Your last tested pieces can start the full construction. An existing draft there keeps its own pieces.

An input that gives the weight no influence

This check uses the pieces from “Connect a labelled example to one weight update”.

BOTIE

The prediction is input times weight, and this example has a zero input with a nonzero target. Take one gradient step on half squared error. Return the new weight.
Training input
0
Current weight
3
Training label
5
Learning rate
0.2

Use a number, text, or an array matching the requested result. For a matrix, put each row in brackets. Saving your prediction runs your current construction on these inputs and checks the earlier examples too.

Build a construction in the workspace above first. This case will test those pieces.

Which value must be fed back as the current weight before a second learning step?

Training repeats state updates and evaluates progress separately from performing any one update.

This is a small construction problem. The lesson explains the assumptions and the parts of the full method that this example leaves out.

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