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Neural Networks

Stop a useful weight growing forever

BOTIE

Multiply the squared current response by the current weight vector.
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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

Multiply the squared current response by the current weight vector.

A connection that strengthens whenever input and output occur together can keep growing. Oja's adjustment adds a stabilising term. Let's build that weight change and inspect how it depends on both the current input and the response the current weights produce.

Inspect the component calculation
Multiply(
  Value: Square(
    Value or list: Dot product(
      First vector: Current weights
      Second vector: Input vector
    )
  )
  Multiplier: Current weights
)
Examples and results
Current weights
  1. 00.6
  2. 10.8
Input vector
  1. 01
  2. 12
Required result
  1. 02.904
  2. 13.872
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.

A new observation points beyond the current axis

This check uses the pieces from “Combine reinforcement with a stabilising correction”.

BOTIE

The current weight vector points along the first coordinate. Return Oja's weight increment for this observation with the workshop's learning rate of 0.1. Return the increment, not the updated weights.
Current weights
  1. 01
  2. 10
Input vector
  1. 01
  2. 13

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.

Why is one computed change insufficient evidence that the weights now represent a principal component?

A learning rule's long-run interpretation depends on its data assumptions and repeated updates.

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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