8 minute interactive lab

Backpropagation

Who gets blamed for a wrong answer?

YOU’LL LEAVE KNOWINGThe chain rule assigns each weight its share of the error.

THE EXPERIMENT

Trace responsibility through the network.

Move the controls. Watch the internal state respond. The explanation follows the behavior—not the other way around.

Runs the real small-scale equationThe displayed values are calculated from the formula shown in this lesson.

BACKWARD PASSSend the gradient backward

Desired output85%

This uses sigmoid plus binary cross-entropy: dL/dz = prediction − target, then dL/dwᵢ = dL/dz × hᵢ.

prediction64%

→

target85%

h10.9

dL/dw -0.187

w10.70

h20.5

dL/dw -0.104

w2-0.25

h30.2

dL/dw -0.042

w30.40

cross-entropy · dL/dz0.531 · -0.208

THE MENTAL MODEL

The chain rule assigns each weight its share of the error.

Backpropagation starts with the output error and works backward. The chain rule measures how sensitive the result was to every activation and weight, assigning larger updates to paths that mattered more.

IN DEVELOPER TERMSgradient_w = error × local_sensitivity

GO DEEPER

Check the model against the source.

Connectionism optimizes for intuition, then points you to the rigorous treatment.

NEXT CONNECTION

How does meaning become geometry?

Embeddings

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